Welcome, dear ASSEB Class 11 students. In this lesson we will study Chapter 4: Conversion of Ordinary Sentences into Logical Propositions from your Class 11 Logic and Philosophy textbook (English Medium). This chapter is one of the most important and most frequently asked sections of the syllabus because almost every annual examination contains questions in which a list of ordinary sentences is given and you are asked to reduce each sentence into its strict logical form (A, E, I, or O). The purpose of this chapter is to teach you how to translate everyday English sentences, with all their grammatical irregularities, into the four standard categorical forms used in deductive logic. Below you will find a complete explanation of all the rules, a long set of textbook-style worked examples, additional questions for examination practice, and a glossary of the technical terms.
Chapter Summary
Ordinary language is rich, flexible and often ambiguous, but the science of logic requires every proposition to be expressed in a fixed, exact and unambiguous form. The four standard logical propositions used in traditional or Aristotelian logic are A (Universal Affirmative – All S are P), E (Universal Negative – No S is P), I (Particular Affirmative – Some S are P) and O (Particular Negative – Some S are not P). Any sentence that we use in daily life must be reduced to one of these four forms before it can be tested for validity, opposed, converted, obverted, or used in syllogisms. The process by which an ordinary sentence is rewritten into one of the four forms (A / E / I / O) is called reduction, transformation or conversion of an ordinary sentence into a logical proposition.
The standard logical form of a categorical proposition consists of four parts arranged in a strict order: Quantifier + Subject term + Copula + Predicate term. The quantifier (All, No, Some) shows quantity. The copula must always be a present tense form of the verb “to be” (is, am, are). The subject term and predicate term must both be class terms (nouns or noun phrases). Adjectives, adverbs, hidden quantifiers, exclusive words, exceptive words, and indefinite expressions all have to be carefully interpreted before the sentence can be put into this form. The chapter therefore lays down a number of rules for handling each kind of irregular sentence and supports each rule with examples.
Why Reduce Sentences to Standard Logical Form?
The reduction of ordinary sentences to logical propositions is necessary for several reasons:
- Logic is a science of arguments, and an argument can be tested only when its propositions are stated unambiguously.
- The four standard forms (A, E, I, O) provide a fixed framework in which the relations of opposition, conversion, obversion and contraposition can be carried out.
- The same idea may be expressed in many grammatical forms in ordinary language; reducing them to one form removes ambiguity.
- The validity of a syllogism depends on the form of the proposition, not the words used. Reduction makes the form visible.
- Hidden quantity (universal or particular) and hidden quality (affirmative or negative) of an ordinary sentence become explicit only after reduction.
Standard Logical Form of a Proposition
The standard form is:
Quantifier + Subject (S) + Copula + Predicate (P)
| Symbol | Name | Standard Form | Quantity | Quality |
|---|---|---|---|---|
| A | Universal Affirmative | All S are P | Universal | Affirmative |
| E | Universal Negative | No S is P | Universal | Negative |
| I | Particular Affirmative | Some S are P | Particular | Affirmative |
| O | Particular Negative | Some S are not P | Particular | Negative |
The Main Rules of Reduction
Rule 1: Identify the Copula
The copula must always be a present-tense form of “to be” (is/am/are). In ordinary sentences the copula is often hidden inside the main verb. Replace such verbs with “is/are” + a participial phrase. Example: “Birds fly” becomes “Birds are flying creatures” or “All birds are creatures that fly”.
Rule 2: Find the Real Subject and Predicate
The subject must be a noun or noun phrase representing a class. Adjectives and adverbs cannot be the subject of a logical proposition. “Honest are respected” must be expanded as “All honest persons are persons who are respected”.
Rule 3: Supply the Missing Quantifier
If the quantifier is not stated, supply it according to the meaning. A general statement of nature or law is universal (A or E); a statement about some individuals is particular (I or O).
Rule 4: Adjective and Adverb Sentences
Adjectives must be turned into noun phrases by adding “persons”, “things”, “men”, etc. Adverbs must be turned into corresponding noun phrases or absorbed into the predicate.
Rule 5: Negative Sentences
If the entire predicate is denied of the entire subject, the proposition is E (No S is P). If the predicate is denied only of a part of the subject, the proposition is O (Some S are not P).
Rule 6: Exclusive Sentences (“Only”, “None but”, “Alone”)
Exclusive sentences such as “Only X are Y” or “None but X are Y” are reduced to A propositions, but the subject and predicate are interchanged. “Only the brave deserve the fair” becomes “All persons who deserve the fair are brave persons” (A).
Rule 7: Exceptive Sentences (“All except”, “All but”)
If the number of exceptions is definite (e.g. “All but two”), the sentence is reduced to two propositions: an A about those included and an E about those excepted. If the number is indefinite (e.g. “All except a few”), reduce to an I proposition (Some S are P).
Rule 8: “Few”, “A few”, “The few” Distinction
This is one of the most important rules of the chapter:
- Few means “almost none”. It carries a negative force and the proposition is reduced to O (Some S are not P).
- A few means “some”. The proposition is reduced to I (Some S are P).
- The few means “all of the small number”. The proposition is reduced to A (All S are P).
Rule 9: “Any”, “Every”, “Each”
These words signify universality. Affirmative sentences with these words are reduced to A; negative ones to E.
Rule 10: Singular Sentences
A singular sentence (whose subject is a particular individual or proper noun) is treated as Universal — A if affirmative, E if negative — because the predicate is asserted (or denied) of the whole subject.
Rule 11: “Always” and “Never”
“Always” indicates universality of time and is treated as a universal quantifier — affirmative form gives A, negative form gives E. “Never” gives an E proposition.
Rule 12: The Definite Article “The”
“The” before a singular noun makes it definite and the sentence is universal. “The cow is a useful animal” becomes “All cows are useful animals” (A).
Rule 13: Words with Negative Force
Words like “seldom”, “scarcely”, “hardly”, “rarely” mean “almost never” and carry negative force. Affirmative-looking sentences with these words are reduced to O (Some S are not P).
Rule 14: “Almost all”, “Most”, “Many”, “A few”, “Certain”, “Several”
These indicate particular quantity in the affirmative — reduce to I (Some S are P). In the negative, reduce to O.
Textbook Questions and Answers (Worked Examples)
Q1. What is meant by reduction of an ordinary sentence into a logical proposition?
Answer: Reduction or transformation of an ordinary sentence into a logical proposition means the process of restating an ordinary sentence in one of the four standard logical forms — A, E, I or O. The reduced proposition has a fixed structure: Quantifier + Subject + Copula + Predicate. The copula must be a present tense form of the verb “to be”. The subject and predicate must be class terms. The reduction makes the quantity and quality of the proposition explicit so that it can be used for further logical operations such as opposition, conversion and syllogistic inference.
Q2. Why is it necessary to reduce ordinary sentences to logical propositions?
Answer: It is necessary because (i) ordinary language is ambiguous while logic requires precision; (ii) the validity of an argument depends on the form of its propositions, and only the four standard forms have fixed logical relations; (iii) hidden quantifiers and hidden negation must be made explicit before any logical inference can be drawn; (iv) operations like opposition, conversion, obversion and syllogistic reasoning can be applied only to standard-form propositions; (v) reduction prevents fallacies that arise from the loose use of words.
Q3. State the standard logical form of a proposition.
Answer: The standard logical form is Quantifier + Subject + Copula + Predicate. Quantifier shows whether the proposition is universal (“All”, “No”) or particular (“Some”). Subject and predicate are class terms. Copula is always a present tense form of the verb “to be” (is/are). The four standard forms are: A — All S are P; E — No S is P; I — Some S are P; O — Some S are not P.
Q4. Reduce: “Birds fly”.
Answer: The verb “fly” hides the copula. Supplying “is/are” and a noun-phrase predicate, and supplying the missing universal quantifier: All birds are creatures that fly (A proposition).
Q5. Reduce: “Honest are respected”.
Answer: “Honest” is an adjective and cannot be the subject of a logical proposition. Convert it into a noun phrase by adding “persons”: All honest persons are persons who are respected (A proposition).
Q6. Reduce: “Only graduates are eligible for this post”.
Answer: An exclusive proposition introduced by “Only”. The subject and predicate are interchanged on reduction: All persons eligible for this post are graduates (A proposition).
Q7. Reduce: “None but the brave deserve the fair”.
Answer: “None but” is an exclusive expression equivalent to “Only”. Therefore: All persons who deserve the fair are brave persons (A proposition).
Q8. Reduce: “Few men are free from selfishness”.
Answer: “Few” means “almost none” and carries a negative force. Therefore: Some men are not free from selfishness (O proposition).
Q9. Reduce: “A few students passed the examination”.
Answer: “A few” means “some”. Therefore: Some students are persons who passed the examination (I proposition).
Q10. Reduce: “The few students who attended the class were attentive”.
Answer: “The few” means “all of those few”. Therefore: All students who attended the class are attentive students (A proposition).
Q11. Reduce: “All except two boys passed the test”.
Answer: Exceptive proposition with a definite number of exceptions. Reduce into two propositions: (i) All boys other than the two are persons who passed (A); (ii) No two boys (the excepted ones) are persons who passed (E).
Q12. Reduce: “All but a few candidates were selected”.
Answer: The number of exceptions is indefinite (“a few”), therefore reduce to a particular proposition: Some candidates are persons who were selected (I proposition).
Q13. Reduce: “Every man is mortal”.
Answer: “Every” is universal. All men are mortal beings (A proposition).
Q14. Reduce: “Each soldier is brave”.
Answer: “Each” is universal. All soldiers are brave persons (A proposition).
Q15. Reduce: “Any student can answer this question”.
Answer: “Any” is universal in this affirmative sentence. All students are persons who can answer this question (A proposition).
Q16. Reduce: “Alexander was a great conqueror”.
Answer: A singular sentence is treated as universal: Alexander is a great conqueror (A proposition).
Q17. Reduce: “Socrates is not a Roman”.
Answer: A singular negative sentence is universal negative: Socrates is not a Roman (E proposition).
Q18. Reduce: “Lions never drink coffee”.
Answer: “Never” gives universal negative quantity: No lion is a creature that drinks coffee (E proposition).
Q19. Reduce: “Scholars are always honoured”.
Answer: “Always” gives universality. All scholars are persons who are honoured (A proposition).
Q20. Reduce: “The cow is a useful animal”.
Answer: The definite article “the” before a generic noun makes it universal: All cows are useful animals (A proposition).
Q21. Reduce: “Triangles can never be squares”.
Answer: “Never” makes it universal negative: No triangle is a square (E proposition).
Q22. Reduce: “Almost all Indians are religious”.
Answer: “Almost all” implies particular quantity affirmative: Some Indians are religious persons (I proposition).
Q23. Reduce: “Most students attend classes regularly”.
Answer: “Most” is treated as particular: Some students are persons who attend classes regularly (I proposition).
Q24. Reduce: “Many people are dishonest”.
Answer: “Many” is particular: Some people are dishonest persons (I proposition).
Q25. Reduce: “Seldom does a wise man err”.
Answer: “Seldom” carries a negative force. Some wise men are not persons who err (O proposition).
Q26. Reduce: “Hardly any boy is fit for this work”.
Answer: “Hardly any” carries a negative force. Some boys are not persons fit for this work (O proposition).
Q27. Reduce: “Wise men are generally flexible”.
Answer: “Generally” indicates particular quantity. Some wise men are flexible persons (I proposition).
Q28. Reduce: “All swans are not white”.
Answer: The negation here applies only to part of the subject (it does not mean “no swan is white” but “not all swans are white”): Some swans are not white birds (O proposition).
Q29. Reduce: “No man is perfect”.
Answer: Already in standard form: No man is a perfect being (E proposition).
Q30. Reduce: “Children love sweets”.
Answer: A general statement supplied with a universal quantifier: All children are lovers of sweets (A proposition).
Q31. Reduce: “Some students did not pass”.
Answer: Already in O form: Some students are not persons who passed (O proposition).
Q32. Reduce: “He who hesitates is lost”.
Answer: The relative-clause construction must be turned into a class term: All persons who hesitate are persons who are lost (A proposition).
Q33. Reduce: “Roses are red”.
Answer: Supply universal quantifier and copula: All roses are red flowers (A proposition).
Q34. Reduce: “Iron rusts”.
Answer: Universal natural law. All iron is a substance that rusts (A proposition).
Q35. Reduce: “None of the answers is correct”.
Answer: “None” gives universal negative: No answer is a correct answer (E proposition).
Q36. Reduce: “Only the wise are happy”.
Answer: Exclusive proposition with subject-predicate interchange: All happy persons are wise persons (A proposition).
Q37. Reduce: “All learned persons are honoured everywhere”.
Answer: Already universal affirmative; absorb the adverb into the predicate: All learned persons are persons who are honoured everywhere (A proposition).
Q38. Reduce: “Few politicians are honest”.
Answer: “Few” is negative in force: Some politicians are not honest persons (O proposition).
Q39. Reduce: “A few politicians are honest”.
Answer: “A few” means “some”: Some politicians are honest persons (I proposition).
Q40. Reduce: “The few politicians who entered the meeting were honest”.
Answer: “The few” means “all of those few”: All politicians who entered the meeting are honest persons (A proposition).
Comprehensive Worked-Example Tables
Table A — Implicit Quantifier and Copula
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Birds fly | All birds are creatures that fly | A |
| Iron rusts | All iron is a substance that rusts | A |
| Roses are red | All roses are red flowers | A |
| Children love sweets | All children are lovers of sweets | A |
| Dogs bark | All dogs are animals that bark | A |
| Fire burns | All fire is a thing that burns | A |
| Snakes bite | All snakes are creatures that bite | A |
Table B — Adjective and Adverb Sentences
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Honest are respected | All honest persons are persons who are respected | A |
| Wise are happy | All wise persons are happy persons | A |
| Brave are admired | All brave persons are persons who are admired | A |
| The poor are unhappy | All poor persons are unhappy persons | A |
| The rich are powerful | All rich persons are powerful persons | A |
| The good are loved | All good persons are persons who are loved | A |
Table C — Exclusive Sentences (Only / None but / Alone)
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Only graduates are eligible | All eligible persons are graduates | A |
| None but the brave deserve the fair | All persons who deserve the fair are brave persons | A |
| Only the wise are happy | All happy persons are wise persons | A |
| None but fools rush in | All persons who rush in are fools | A |
| The labourer alone is worthy of his hire | All persons worthy of their hire are labourers | A |
| Only the male can enter the mosque | All persons who enter the mosque are male persons | A |
| Only the uneducated are superstitious | All superstitious persons are uneducated persons | A |
Table D — Exceptive Sentences (All except / All but)
| Ordinary Sentence | Reduced Form(s) | Type |
|---|---|---|
| All except two boys passed | All boys other than the two are persons who passed; No two excepted boys are persons who passed | A + E |
| All but three students were absent | All students other than the three are persons who were absent; No three excepted students are persons who were absent | A + E |
| All except a few were happy | Some persons are happy persons | I |
| All but a few candidates were selected | Some candidates are persons who were selected | I |
| All except some are present | Some persons are present | I |
Table E — Few / A few / The few
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Few politicians are honest | Some politicians are not honest persons | O |
| Few men are free from selfishness | Some men are not persons free from selfishness | O |
| A few politicians are honest | Some politicians are honest persons | I |
| A few students passed | Some students are persons who passed | I |
| The few politicians who came were honest | All politicians who came are honest persons | A |
| The few survivors were rescued | All survivors are persons who were rescued | A |
Table F — Any / Every / Each
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Every man is mortal | All men are mortal beings | A |
| Each soldier is brave | All soldiers are brave persons | A |
| Any student can solve this | All students are persons who can solve this | A |
| Every effort was successful | All efforts are successful efforts | A |
| Each apple in this basket is ripe | All apples in this basket are ripe apples | A |
Table G — Singular Sentences
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Alexander was a great conqueror | Alexander is a great conqueror | A |
| Socrates is wise | Socrates is a wise person | A |
| Socrates is not a Roman | Socrates is not a Roman | E |
| Mount Everest is the highest peak | Mount Everest is the highest peak | A |
| Gandhi was a great leader | Gandhi is a great leader | A |
| Ravi is not a doctor | Ravi is not a doctor | E |
Table H — Always / Never / Universal Time
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Scholars are always honoured | All scholars are persons who are honoured | A |
| Lions never drink coffee | No lion is a creature that drinks coffee | E |
| Triangles can never be squares | No triangle is a square | E |
| Honest men always speak the truth | All honest men are persons who speak the truth | A |
| A liar is never trusted | No liar is a person who is trusted | E |
Table I — Definite Article “The”
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| The cow is a useful animal | All cows are useful animals | A |
| The horse is a quadruped | All horses are quadrupeds | A |
| The dog is faithful | All dogs are faithful animals | A |
| The lion is the king of beasts | All lions are kings of beasts | A |
Table J — Words with Negative Force
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Seldom does a wise man err | Some wise men are not persons who err | O |
| Hardly any student failed | Some students are not persons who failed | O |
| Scarcely any answer was correct | Some answers are not correct answers | O |
| Rarely is honesty rewarded | Some instances of honesty are not rewarded instances | O |
Table K — Most / Many / Almost all / Generally
| Ordinary Sentence | Logical Form | Type |
|---|---|---|
| Most students study hard | Some students are hard-studying students | I |
| Many people are kind | Some people are kind persons | I |
| Almost all Indians are religious | Some Indians are religious persons | I |
| Almost all birds can fly | Some birds are creatures that can fly | I |
| Wise men are generally flexible | Some wise men are flexible persons | I |
| Several boys were absent | Some boys are persons who were absent | I |
| Certain answers are wrong | Some answers are wrong answers | I |
Additional Questions and Answers
Q41. Why is the copula always in the present tense?
Answer: Because logic studies the timeless or general relation between subject and predicate. A past or future tense would tie the proposition to a particular time and would prevent generalisation. Therefore, in the standard logical form, the verb is replaced by a present tense form of “to be” (is/are) so that the relation between subject class and predicate class is expressed in a timeless manner.
Q42. Why are exclusive sentences reduced to A propositions?
Answer: Because the word “Only” or “None but” actually states that the predicate of the sentence is true of no class except the one named. In other words, the predicate is the wider class and the subject is the narrower class. Therefore “Only X are Y” really means “All Y are X” — a Universal Affirmative or A proposition.
Q43. Distinguish between “few”, “a few” and “the few” with examples.
Answer: “Few” means “almost none” and is negative in force; the proposition is reduced to O. Example: “Few men are perfect” → “Some men are not perfect persons” (O). “A few” means “some”; the proposition is reduced to I. Example: “A few men are perfect” → “Some men are perfect persons” (I). “The few” means “all of that small number”; the proposition is reduced to A. Example: “The few men who came were perfect” → “All men who came are perfect persons” (A).
Q44. How is an exceptive proposition with a definite number of exceptions reduced?
Answer: Such a proposition is reduced to two separate logical propositions — an A about those included and an E about those excepted. For example, “All except three students passed” becomes (i) “All students other than the three are persons who passed” (A) and (ii) “No three excepted students are persons who passed” (E).
Q45. Reduce: “All that glitters is not gold”.
Answer: The negation does not apply to the entire subject but only to part of it. The sentence really means “Not everything that glitters is gold”. Therefore: Some things that glitter are not gold (O proposition).
Q46. Reduce: “Lions are not vegetarians”.
Answer: Universal negative: No lion is a vegetarian (E proposition).
Q47. Reduce: “Some students are not present”.
Answer: Already in O form: Some students are not persons who are present (O proposition).
Q48. Reduce: “He alone is great who is good”.
Answer: Exclusive expression with “alone”: All great persons are good persons (A proposition).
Q49. Reduce: “No student of this class is below sixteen”.
Answer: Already standard E: No student of this class is a person below sixteen (E proposition).
Q50. Reduce: “All work and no play makes Jack a dull boy”.
Answer: The proverb is general. All boys who only work and never play are dull boys (A proposition).
Q51. Reduce: “Some students of this class are intelligent”.
Answer: Already in I form: Some students of this class are intelligent students (I proposition).
Q52. Reduce: “Not all snakes are poisonous”.
Answer: The negation is partial. Some snakes are not poisonous creatures (O proposition).
Q53. Reduce: “Whatever is, is right”.
Answer: The relative-clause “whatever is” is the subject. All things that exist are right things (A proposition).
Q54. Reduce: “All teachers are not rich”.
Answer: Negation is partial: Some teachers are not rich persons (O proposition).
Q55. Reduce: “There are black swans”.
Answer: An existential affirmative is treated as I: Some swans are black birds (I proposition).
Q56. Reduce: “There is no smoke without fire”.
Answer: Universal negative form: No smoke is a smoke without fire, or equivalently, All smoke is smoke with fire (A proposition). Either form is accepted.
Q57. State the common errors students make in reduction.
Answer: The common errors are: (i) treating “few” as I instead of O; (ii) failing to interchange subject and predicate in exclusive propositions; (iii) treating exceptive sentences with definite numbers as a single proposition; (iv) keeping the original verb instead of supplying “is/are” as copula; (v) leaving an adjective as the subject; (vi) supplying a particular quantifier where universal is meant (e.g. “Iron rusts” should be A, not I); (vii) treating singular sentences as particular instead of universal; (viii) misreading “All S are not P” as E when it actually means O; (ix) missing the negative force of “seldom”, “hardly”, “scarcely”.
Q58. Reduce: “All but the foolish admit their mistakes”.
Answer: The number of the excepted (“the foolish”) is indefinite as a class. Reduce as: All persons who are not foolish are persons who admit their mistakes (A proposition); and No foolish persons are persons who admit their mistakes (E proposition).
Q59. Reduce: “He is rarely absent”.
Answer: “Rarely” carries negative force on a singular subject. He is not (generally) a person who is absent (E proposition; singular negative).
Q60. Reduce: “Each one of us is responsible”.
Answer: “Each” is universal. All of us are responsible persons (A proposition).
Common Errors to Avoid
- Do not treat “Few” as if it meant “Some”; “Few” is negative in force and gives O.
- Do not forget to interchange subject and predicate in “Only” and “None but” sentences.
- Do not keep the active verb; always use is/am/are as copula.
- Do not leave an adjective as a subject; convert it into a noun phrase.
- Do not read “All S are not P” as E; it is O (partial negation).
- Do not treat singular sentences as particular; they are universal (A or E).
- Do not forget the two propositions required when an exceptive proposition has a definite exception.
- Do not ignore the universal force of “always”, “never”, “every”, “each”, “any”.
- Do not treat “almost all”, “most”, “many”, “generally” as universal — they are particular.
Glossary
| Term | Meaning |
|---|---|
| Reduction / Transformation | The process of restating an ordinary sentence in one of the four standard forms A, E, I, O. |
| Categorical Proposition | A proposition that asserts or denies a predicate of a subject without condition. |
| Quantifier | A word like “All”, “No” or “Some” that shows the quantity of the proposition. |
| Subject term (S) | The class about which something is asserted or denied. |
| Predicate term (P) | The class that is asserted or denied of the subject. |
| Copula | The verb (is/are) connecting subject and predicate; always present tense. |
| A proposition | Universal Affirmative — All S are P. |
| E proposition | Universal Negative — No S is P. |
| I proposition | Particular Affirmative — Some S are P. |
| O proposition | Particular Negative — Some S are not P. |
| Exclusive proposition | A sentence containing “Only”, “None but”, “Alone”; reduced to A with subject-predicate interchange. |
| Exceptive proposition | A sentence containing “All except”, “All but”; reduced to A+E if exceptions are definite, to I if indefinite. |
| Singular proposition | A proposition whose subject is a single individual; treated as universal (A or E). |
| Definite article rule | “The” + singular noun representing a class makes the proposition universal. |
| Negative-force words | Words like Few, Seldom, Scarcely, Hardly, Rarely; carry hidden negation; reduce to O. |
| Particular-force words | Words like A few, Most, Many, Almost all, Generally, Several, Certain; reduce to I. |
| Universal-force words | Words like All, Every, Each, Any, Always, Never, None; reduce to A or E. |
Final Worked-Examples Quick-Reference Table
| No. | Ordinary Sentence | Logical Form | Type |
|---|---|---|---|
| 1 | Birds fly | All birds are creatures that fly | A |
| 2 | Honest are respected | All honest persons are persons who are respected | A |
| 3 | Only graduates are eligible | All eligible persons are graduates | A |
| 4 | None but the brave deserve the fair | All persons who deserve the fair are brave persons | A |
| 5 | Few men are free from selfishness | Some men are not persons free from selfishness | O |
| 6 | A few students passed | Some students are persons who passed | I |
| 7 | The few survivors were rescued | All survivors are persons who were rescued | A |
| 8 | All except two boys passed | All boys other than the two passed (A); No two excepted boys passed (E) | A+E |
| 9 | All but a few were selected | Some persons are persons who were selected | I |
| 10 | Every man is mortal | All men are mortal beings | A |
| 11 | Each soldier is brave | All soldiers are brave persons | A |
| 12 | Any student can solve this | All students are persons who can solve this | A |
| 13 | Alexander was a great conqueror | Alexander is a great conqueror | A |
| 14 | Socrates is not a Roman | Socrates is not a Roman | E |
| 15 | Lions never drink coffee | No lion is a creature that drinks coffee | E |
| 16 | Scholars are always honoured | All scholars are persons who are honoured | A |
| 17 | The cow is a useful animal | All cows are useful animals | A |
| 18 | Triangles can never be squares | No triangle is a square | E |
| 19 | Almost all Indians are religious | Some Indians are religious persons | I |
| 20 | Most students study hard | Some students are hard-studying students | I |
| 21 | Many people are kind | Some people are kind persons | I |
| 22 | Seldom does a wise man err | Some wise men are not persons who err | O |
| 23 | Hardly any student failed | Some students are not persons who failed | O |
| 24 | Wise men are generally flexible | Some wise men are flexible persons | I |
| 25 | All swans are not white | Some swans are not white birds | O |
| 26 | No man is perfect | No man is a perfect being | E |
| 27 | Children love sweets | All children are lovers of sweets | A |
| 28 | He who hesitates is lost | All persons who hesitate are persons who are lost | A |
| 29 | Roses are red | All roses are red flowers | A |
| 30 | Iron rusts | All iron is a substance that rusts | A |
| 31 | None of the answers is correct | No answer is a correct answer | E |
| 32 | Only the wise are happy | All happy persons are wise persons | A |
| 33 | Few politicians are honest | Some politicians are not honest persons | O |
| 34 | A few politicians are honest | Some politicians are honest persons | I |
| 35 | The few politicians who came were honest | All politicians who came are honest persons | A |
| 36 | Whatever is, is right | All things that exist are right things | A |
| 37 | All teachers are not rich | Some teachers are not rich persons | O |
| 38 | There are black swans | Some swans are black birds | I |
| 39 | All work and no play makes Jack a dull boy | All boys who only work and never play are dull boys | A |
| 40 | Each one of us is responsible | All of us are responsible persons | A |
Extended Practice Set 1 — Mixed Sentences with Step-by-Step Reasoning
Q61. Reduce: “Books are men’s best friends”.
Answer: The sentence is general; supply the universal quantifier “All”. The verb “are” is already the copula. The predicate “men’s best friends” is a noun phrase, so no further change is needed. Logical form: All books are men’s best friends (A proposition).
Q62. Reduce: “Knowledge is power”.
Answer: A general proverbial statement. Supply universal quantifier and treat the abstract noun as the subject class. Logical form: All knowledge is power (A proposition).
Q63. Reduce: “Some metals are not heavy”.
Answer: Already in O form. Logical form: Some metals are not heavy substances (O proposition).
Q64. Reduce: “There are honest persons in the world”.
Answer: Existential affirmative. Logical form: Some persons in the world are honest persons (I proposition).
Q65. Reduce: “There are no honest politicians”.
Answer: Existential negative is treated as universal negative. Logical form: No politicians are honest persons (E proposition).
Q66. Reduce: “Wise men are not always rich”.
Answer: “Not always” indicates partial negation. Logical form: Some wise men are not rich persons (O proposition).
Q67. Reduce: “Diamonds are precious stones”.
Answer: Universal natural fact. Logical form: All diamonds are precious stones (A proposition).
Q68. Reduce: “Boys will be boys”.
Answer: A timeless general truth. Logical form: All boys are boys (A proposition; tautological but valid).
Q69. Reduce: “Snakes do not have legs”.
Answer: Universal negation. Logical form: No snake is a creature that has legs (E proposition).
Q70. Reduce: “Some apples are sweet”.
Answer: Already in I form. Logical form: Some apples are sweet fruits (I proposition).
Q71. Reduce: “Heavy is the head that wears a crown”.
Answer: The adjective “heavy” cannot be the subject; the real subject is “the head that wears a crown”. Logical form: All heads that wear a crown are heavy heads (A proposition).
Q72. Reduce: “Blessed are the meek”.
Answer: “Blessed” is an adjective that cannot be the subject; the real subject is “the meek”. Logical form: All meek persons are blessed persons (A proposition).
Q73. Reduce: “Truth is mighty and shall prevail”.
Answer: Compound but generally treated as a single A proposition. Logical form: All truth is a mighty thing that shall prevail (A proposition).
Q74. Reduce: “Some politicians are dishonest”.
Answer: Already in I form. Logical form: Some politicians are dishonest persons (I proposition).
Q75. Reduce: “All metals do not conduct electricity”.
Answer: The negation is partial (some do, some do not). Logical form: Some metals are not conductors of electricity (O proposition).
Q76. Reduce: “All but five candidates were selected”.
Answer: Definite exception, so reduce to two propositions. (i) All candidates other than the five are persons who were selected (A); (ii) No five excepted candidates are persons who were selected (E).
Q77. Reduce: “All except the lazy succeed”.
Answer: The exception (“the lazy”) is a class. Reduce as: (i) All non-lazy persons are persons who succeed (A); (ii) No lazy persons are persons who succeed (E).
Q78. Reduce: “All save one returned”.
Answer: Definite numerical exception. (i) All persons other than the one are persons who returned (A); (ii) The one excepted person is not a person who returned (E).
Q79. Reduce: “Only educated women are good citizens”.
Answer: Exclusive proposition with subject-predicate interchange. Logical form: All good citizens are educated women (A proposition).
Q80. Reduce: “None but a fool would believe this”.
Answer: Exclusive proposition. Logical form: All persons who would believe this are fools (A proposition).
Extended Practice Set 2 — More Worked Examples
| No. | Ordinary Sentence | Logical Form | Type |
|---|---|---|---|
| 81 | Liars are never trusted | No liars are persons who are trusted | E |
| 82 | The brave deserve the fair | All brave persons are persons who deserve the fair | A |
| 83 | Some of these students are absent | Some of these students are persons who are absent | I |
| 84 | Few are chosen | Some persons are not persons who are chosen | O |
| 85 | Many are called | Some persons are persons who are called | I |
| 86 | The poor are always with us | All poor persons are persons who are always with us | A |
| 87 | Wisdom is rare | All wisdom is a rare quality | A |
| 88 | Time and tide wait for none | No time and tide is a thing that waits for any person | E |
| 89 | Pride goes before a fall | All instances of pride are things that go before a fall | A |
| 90 | Genius is one per cent inspiration and ninety-nine per cent perspiration | All genius is one per cent inspiration and ninety-nine per cent perspiration | A |
| 91 | Honesty is the best policy | All honesty is the best policy | A |
| 92 | Practice makes a man perfect | All persons who practise are persons who become perfect | A |
| 93 | Barking dogs seldom bite | Some barking dogs are not creatures that bite | O |
| 94 | An empty vessel sounds much | All empty vessels are vessels that sound much | A |
| 95 | A rolling stone gathers no moss | No rolling stone is a stone that gathers moss | E |
| 96 | Cowards die many times before their death | All cowards are persons who die many times before their death | A |
| 97 | Brevity is the soul of wit | All brevity is the soul of wit | A |
| 98 | The pen is mightier than the sword | All instances of the pen are things mightier than the sword | A |
| 99 | Necessity is the mother of invention | All necessity is the mother of invention | A |
| 100 | Rome was not built in a day | Rome is not a city built in a day | E |
| 101 | Some of my friends are not present | Some of my friends are not persons who are present | O |
| 102 | None of the boys is absent | No boy is a person who is absent | E |
| 103 | Hardly anyone is satisfied | Some persons are not persons who are satisfied | O |
| 104 | The good die young | All good persons are persons who die young | A |
| 105 | Idleness is the mother of all vices | All idleness is the mother of all vices | A |
| 106 | Most candidates failed | Some candidates are persons who failed | I |
| 107 | Almost no one came | Some persons are not persons who came | O |
| 108 | Several books are missing | Some books are missing books | I |
| 109 | Certain matters are confidential | Some matters are confidential matters | I |
| 110 | Each of you is responsible for the result | All of you are persons responsible for the result | A |
| 111 | Anybody can do this | All persons are persons who can do this | A |
| 112 | Anyone who works hard succeeds | All persons who work hard are persons who succeed | A |
| 113 | Everybody loves a winner | All persons are persons who love a winner | A |
| 114 | Nobody is perfect | No person is a perfect being | E |
| 115 | Nothing is impossible | No thing is an impossible thing | E |
| 116 | Few but the brave deserve the fair | All persons who deserve the fair are brave persons | A |
| 117 | Almost every student attended | Some students are persons who attended | I |
| 118 | Not a single student was present | No student is a person who was present | E |
| 119 | Hardly a man is present | Some men are not persons who are present | O |
| 120 | The sun rises in the east | All instances of the sun’s rising are events in the east | A |
Extended Practice Set 3 — Detailed Analysis Questions
Q121. Why is the sentence “Few men are honest” different from “A few men are honest”?
Answer: Although both sentences look similar, they differ in logical meaning and force. “Few men are honest” implies that the number of honest men is so small as to be almost none, and the emphasis falls on the absence of honesty. The proposition is therefore negative in quality and is reduced to Some men are not honest persons (O). On the other hand, “A few men are honest” affirms the existence of some honest men without any negative implication. The proposition is therefore positive and is reduced to Some men are honest persons (I). The single article “a” makes a fundamental difference in logical force.
Q122. Why is the sentence “All except a few were saved” different from “All except two were saved”?
Answer: The difference lies in the definiteness of the exception. In “All except two”, the number of exceptions is definite (two), so we know exactly which group is included and which is excluded. The sentence is reduced to two propositions: an A about those included and an E about the two who were not saved. In “All except a few”, the number of exceptions is indefinite, so we cannot make a definite universal claim about either group. The sentence is therefore reduced to a single I proposition: Some persons are persons who were saved.
Q123. State the procedure for reducing an ordinary sentence into a logical proposition.
Answer: The procedure may be summarised in the following steps:
- Read the sentence carefully and grasp its full meaning.
- Identify the real subject (a class term, not an adjective).
- Identify the real predicate (also a class term).
- Find or supply the copula in the present tense (is/are).
- Find or supply the quantifier — universal (All/No) or particular (Some).
- Determine quality — affirmative or negative.
- Apply the special rule that fits the type of sentence (exclusive, exceptive, “few” etc.).
- Write the sentence in the order: Quantifier + Subject + Copula + Predicate.
- State the type of proposition (A, E, I or O) at the end.
Q124. Distinguish between a categorical proposition and an ordinary sentence.
Answer: An ordinary sentence is any grammatically correct expression in language; it may be a statement, a question, a command, an exclamation or a wish. It need not have a logical structure. A categorical proposition, on the other hand, is a statement that asserts or denies a predicate of a subject in an unconditional way. It must have four definite parts — quantifier, subject, copula, predicate — and must fall into one of the four classes A, E, I or O. Only a declarative sentence stating a relation between two class terms can be a categorical proposition; not all ordinary sentences are categorical propositions.
Q125. Reduce: “He who fights and runs away may live to fight another day”.
Answer: The relative-clause subject “He who fights and runs away” must be expanded. Logical form: All persons who fight and run away are persons who may live to fight another day (A proposition).
Q126. Reduce: “What cannot be cured must be endured”.
Answer: The relative subject “What cannot be cured” is a class term. Logical form: All things that cannot be cured are things that must be endured (A proposition).
Q127. Reduce: “He laughs best who laughs last”.
Answer: Logical form: All persons who laugh last are persons who laugh best (A proposition).
Q128. Reduce: “All is well that ends well”.
Answer: Logical form: All things that end well are things that are well (A proposition).
Q129. Reduce: “Where there is a will there is a way”.
Answer: Logical form: All cases in which there is a will are cases in which there is a way (A proposition).
Q130. Reduce: “Whoever loves his country is patriotic”.
Answer: Logical form: All persons who love their country are patriotic persons (A proposition).
Q131. Reduce: “Wherever you go, you find pollution”.
Answer: Logical form: All places where you go are places where you find pollution (A proposition).
Q132. Reduce: “Whenever I see him, he is reading a book”.
Answer: Logical form: All times when I see him are times when he is reading a book (A proposition).
Important Examination Tips
- Always state the type of proposition (A, E, I, or O) clearly at the end of your reduction.
- Justify your reduction by naming the rule applied — for example, “Exclusive sentence rule” or “Few rule”.
- For exceptive sentences with definite exceptions, write both propositions; do not stop at one.
- Never leave the verb as a tense verb; always replace with is/are.
- Never leave an adjective as the subject; always supply “persons”, “things”, “men” etc.
- For “All S are not P”, remember it is O, not E.
- For “Only X are Y”, remember subject and predicate are interchanged.
- Watch for hidden negation in “few”, “seldom”, “hardly”, “scarcely”, “rarely”.
- Singular sentences are universal — A if affirmative, E if negative.
- Read the sentence twice before reducing — meaning is more important than grammar.
Bird’s-eye View — Quick Identification Chart
| Word / Pattern | Reduce To | Why |
|---|---|---|
| All / Every / Each / Any (affirmative) | A | Universal affirmative force |
| No / None / Never (universal) | E | Universal negative force |
| Some / A few / Most / Many / Almost all / Generally / Several / Certain | I | Particular affirmative force |
| Some not / Few / Seldom / Hardly / Scarcely / Rarely | O | Particular negative force |
| Only / None but / Alone (subject-predicate interchange) | A | Exclusive proposition |
| All except / All but (definite exception) | A + E | Two parts of exception |
| All except / All but (indefinite exception) | I | Quantity is uncertain |
| The few | A | “All of those few” |
| Singular subject (proper noun) | A or E | Treated as universal |
| The (definite article + class noun) | A | Class generalisation |
| Always (in general statements) | A | Universal in time |
| All S are not P | O | Partial negation only |
Final Practice Set — 30 More Worked Examples
| No. | Ordinary Sentence | Logical Form | Type |
|---|---|---|---|
| 133 | All Indians are not Hindus | Some Indians are not Hindus | O |
| 134 | Hardly any honest man is rich | Some honest men are not rich persons | O |
| 135 | Only those who work shall eat | All persons who shall eat are persons who work | A |
| 136 | The rich are not always happy | Some rich persons are not happy persons | O |
| 137 | Some politicians are honest persons | Some politicians are honest persons | I |
| 138 | Every triangle has three sides | All triangles are figures that have three sides | A |
| 139 | No square is a triangle | No square is a triangle | E |
| 140 | A few flowers in this garden are roses | Some flowers in this garden are roses | I |
| 141 | The few flowers I plucked were roses | All flowers I plucked are roses | A |
| 142 | Few flowers in this garden are fragrant | Some flowers in this garden are not fragrant flowers | O |
| 143 | All but the foolish are wise | All non-foolish persons are wise persons (A); No foolish persons are wise persons (E) | A+E |
| 144 | None of these books is mine | No book among these is a book that is mine | E |
| 145 | Each of these mangoes is sweet | All these mangoes are sweet fruits | A |
| 146 | Any boy can win this prize | All boys are persons who can win this prize | A |
| 147 | Almost everyone is selfish | Some persons are selfish persons | I |
| 148 | Scarcely any boy was attentive | Some boys are not persons who were attentive | O |
| 149 | Most teachers are sincere | Some teachers are sincere persons | I |
| 150 | Many people in India are poor | Some people in India are poor persons | I |
| 151 | Several writers attended the conference | Some writers are persons who attended the conference | I |
| 152 | Certain answers are correct | Some answers are correct answers | I |
| 153 | The dog is a faithful animal | All dogs are faithful animals | A |
| 154 | The horse is a noble animal | All horses are noble animals | A |
| 155 | Tigers are carnivorous | All tigers are carnivorous animals | A |
| 156 | Sugar is sweet | All sugar is a sweet substance | A |
| 157 | Salt is necessary for life | All salt is a substance necessary for life | A |
| 158 | Beggars cannot be choosers | No beggars are persons who can be choosers | E |
| 159 | A drowning man catches at a straw | All drowning men are persons who catch at a straw | A |
| 160 | The early bird catches the worm | All early birds are birds that catch the worm | A |
| 161 | Empty vessels make the most noise | All empty vessels are vessels that make the most noise | A |
| 162 | A burnt child dreads the fire | All burnt children are persons who dread the fire | A |
Summary of the Chapter in Brief
The chapter “Conversion of Ordinary Sentences into Logical Propositions” teaches the student how to translate everyday English statements into the four standard categorical forms — A, E, I, O — used in deductive logic. The standard form is built on four parts: Quantifier + Subject + Copula + Predicate, with the copula always in the present tense. Different kinds of ordinary sentences require different rules: implicit quantifiers must be supplied, adjectives must be turned into noun phrases, exclusive sentences (Only, None but) demand subject-predicate interchange and reduce to A, exceptive sentences split into A+E if the exception is definite or reduce to I if it is indefinite, the words Few, Seldom, Scarcely, Hardly carry negative force and reduce to O, A few/Most/Many/Almost all reduce to I, The few reduces to A, singular sentences and statements with the definite article are universal, and Always/Never confer universal quantity. Mastering these rules and practising the worked examples in the tables ensures full marks in this section of the examination.
Dear ASSEB students, this completes the full study of Chapter 4 — Conversion of Ordinary Sentences into Logical Propositions. Practise as many sentences as possible from your textbook, and remember the rules summarised above. Most of the marks in this section come from accurate identification of the type (A, E, I, O), so always justify your answer in the exam by stating the rule that you applied. Best wishes for your examinations.