"Logical Reasoning" — Practice

Question 1

In the categorical proposition "No politicians are saints" (an E form), which terms are distributed?
(a) Only the subject, "politicians"  (b) Only the predicate, "saints"  (c) Both the subject and the predicate  (d) Neither term

Accepted Answer

The E form (universal negative) is the one proposition type that distributes both of its terms — it makes a claim about every member of the subject class (none of them are P) and, symmetrically, about every member of the predicate class (none of them are S either).

Answer: (c) Both the subject and the predicate. Trap (a) captures only the universal-subject half of the rule. Trap (b) captures only the negative-predicate half. Trap (d) forgets that E is precisely the form where both distribution conditions (universal and negative) are satisfied at once.

Question 2

The proposition "All members of the club are volunteers" (A) is confirmed true. What follows about "No members of the club are volunteers" (E)?
(a) It must also be true  (b) It must be false  (c) It could be either true or false  (d) It becomes a particular proposition instead

Accepted Answer

A and E, sharing the same subject and predicate, are contraries — they can both be false, but they can never both be true. Since A has been confirmed true, E is therefore guaranteed false.

Answer: (b) It must be false. Trap (a) violates the defining property of contraries. Trap (c) is only correct for a pair with a weaker relationship than contraries. Trap (d) invents a form change that the square of opposition never produces.

Question 3

"Some voters in the survey are undecided" (I) is established as false. What follows about "Some voters in the survey are not undecided" (O)?
(a) O must be true  (b) O must be false  (c) O could be either true or false  (d) Nothing at all follows about O

Accepted Answer

I and O are subcontraries — they can both be true, but they can never both be false. Since I has been established false, O is therefore guaranteed true.

Answer: (a) O must be true. Trap (b) would require both subcontraries to be false simultaneously, which the relationship forbids. Trap (c) ignores the guarantee subcontraries specifically provide once one member is known false. Trap (d) wrongly claims no inference is possible, when the square of opposition gives one directly.

Question 4

After review, "All interns completed the assignment" (A) is found to be false. What follows with certainty about "Some interns did not complete the assignment" (O)?
(a) O is false  (b) O could be either true or false  (c) Nothing follows about O  (d) O is true

Accepted Answer

A and O, sharing the same subject and predicate, are contradictories — exactly one of the pair is true and the other false, with no third possibility. Since A is false, O must be true.

Answer: (d) O is true. Trap (a) reverses the guaranteed value. Trap (b) denies the certainty that the contradictory relationship specifically provides. Trap (c) wrongly claims the square of opposition gives no information here, when contradictories are in fact its strongest, most certain relationship.

Question 5

Consider: "All engineers are graduates. All graduates are literate. Therefore, all engineers are literate." Is this syllogism valid?
(a) Invalid — illicit major  (b) Valid — this is the classical AAA mood, Barbara  (c) Invalid — fallacy of undistributed middle  (d) Invalid — two negative premises

Accepted Answer

The middle term "graduates" is distributed in the second premise (subject of an A statement), satisfying the middle-term rule. Every term distributed in the conclusion ("engineers" as the distributed subject of an A conclusion) is also distributed in the premise it occurs in. Both premises are affirmative and universal, and the conclusion is affirmative and universal — every rule holds. This is the classical AAA-mood syllogism, traditionally named Barbara.

Answer: (b) Valid — Barbara (AAA). Trap (a) invents a distribution violation that does not occur here — the major term "literate" is undistributed in both the premise and the conclusion, so no illicit major arises. Trap (c) is false since the middle term is distributed once, which is all the rule requires. Trap (d) misdescribes the premises, both of which are affirmative, not negative.

Question 6

Consider: "All dogs are mammals. No cats are dogs. Therefore, no cats are mammals." Is this syllogism valid?
(a) Valid  (b) Invalid — fallacy of undistributed middle  (c) Invalid — illicit major, since "mammals" is distributed in the conclusion but not in either premise  (d) Invalid — two negative premises

Accepted Answer

The major term is "mammals" (the predicate of the conclusion). In the conclusion, "no cats are mammals" is an E statement, which distributes both terms — so "mammals" is distributed there. But in the premise where "mammals" occurs ("All dogs are mammals", an A statement), it sits as the predicate, which an A statement leaves undistributed. A term distributed in the conclusion but not in its own premise commits the illicit major fallacy, making this syllogism invalid despite its true-sounding conclusion.

Answer: (c) Invalid — illicit major. Trap (a) misses the distribution violation entirely. Trap (b) is false — the middle term "dogs" is distributed once (as the subject of the A premise), so the middle-term rule is actually satisfied. Trap (d) misdescribes the premises: only one ("No cats are dogs") is negative, not both.

Question 7

Consider: "No fish are mammals. No mammals are insects. Therefore, no fish are insects." Is this syllogism valid?
(a) Invalid — no valid conclusion can be drawn from two negative premises  (b) Valid, by transitivity of the two negative statements  (c) Invalid — fallacy of four terms  (d) Valid, since both premises happen to be true statements

Accepted Answer

Regardless of how plausible its conclusion sounds, a syllogism built from two negative premises never yields a valid conclusion — this is one of the six fixed validity rules, and it applies here without exception since both premises are E-form negatives.

Answer: (a) Invalid — no valid conclusion from two negative premises. Trap (b) invents a "transitivity" shortcut that categorical syllogisms do not follow. Trap (c) is factually wrong — exactly three terms (fish, mammals, insects) are used consistently. Trap (d) confuses the truth of the premises with the validity of the argument's form — these are entirely separate properties in formal logic.

Question 8

Consider: "Some employees are not managers. Some managers are mentors. Therefore, some employees are not mentors." Is this syllogism valid?
(a) Valid — the syllogism satisfies all six rules  (b) Invalid — this syllogism uses four terms instead of three  (c) Invalid — the conclusion is affirmative but a premise is negative  (d) Invalid — two particular premises can never yield a valid conclusion

Accepted Answer

Both premises are particular statements (one O, one I) rather than universal — and the rule governing categorical syllogisms is that two particular premises can never yield a valid conclusion, regardless of how the terms are otherwise arranged.

Answer: (d) Invalid — two particular premises. Trap (a) misses this violation entirely. Trap (b) is factually wrong — exactly three terms (employees, managers, mentors) recur consistently across the argument. Trap (c) misdescribes the conclusion, which is itself negative ("some employees are not mentors"), matching rather than contradicting the negative premise.

Question 9

On a three-circle Venn diagram (with circles for poets, dreamers, and a third class), how is the universal affirmative proposition "All poets are dreamers" represented?
(a) By shading out the region of the poets circle that lies outside the dreamers circle  (b) By placing an X in the overlap between poets and dreamers  (c) By shading the entire dreamers circle  (d) By placing an X outside both circles

Accepted Answer

Universal claims (A and E forms) are represented on a Venn diagram by shading out the region the claim declares empty. "All poets are dreamers" declares that no poet exists outside the dreamers circle, so that specific region — poets minus dreamers — is shaded out, leaving only the poets-and-dreamers overlap unshaded within the poets circle.

Answer: (a). Trap (b) describes how a particular (I-form) claim is represented, using an X rather than shading. Trap (c) shades a region the proposition never actually claims is empty. Trap (d) places a mark in a region entirely irrelevant to the claim being represented.

Question 10

A student accepts that a particular chemical reaction is exothermic because a trusted textbook states so, without personally observing or testing the reaction. Which pramana does this illustrate?
(a) Pratyaksha  (b) Shabda  (c) Upamana  (d) Anumana

Accepted Answer

Knowledge accepted purely on the word of a reliable, trustworthy source — with no personal observation, inference from a sign, or comparison involved — is the defining structure of Shabda (verbal testimony).

Answer: (b) Shabda. Trap (a) would require direct sensory observation of the reaction, which the question explicitly rules out. Trap (c) would require a previously stated resemblance to another known case, not a source's factual claim. Trap (d) would require inferring an unperceived fact from an observed sign, which is absent here — the fact is simply taken on trust.

Question 11

In the Nyaya five-membered syllogism, the member "The hill has smoke, which is invariably accompanied by fire" — applying the general rule to this specific case — is called:
(a) Pratijna  (b) Hetu  (c) Upanaya  (d) Nigamana

Accepted Answer

Upanaya is specifically the application step: having stated the thesis (Pratijna), the reason (Hetu), and the general rule with its example (Udaharana), the argument now applies that general rule directly to the specific case under discussion, ahead of the final restated conclusion.

Answer: (c) Upanaya. Trap (a), Pratijna, is the initial proposition ("the hill has fire"), stated earlier. Trap (b), Hetu, is the bare reason ("because it has smoke"), without the applied general rule. Trap (d), Nigamana, is the final restated conclusion ("therefore, the hill has fire"), which comes after this step, not at it.

Question 12

A quality inspector examines a random sample of 50 items from a large production batch, finds all 50 defect-free, and concludes the entire batch is very likely defect-free. Separately, a colleague argues a newly installed machine will perform like an older machine already in use, because the two share nearly identical mechanical specifications. Which types of reasoning are these, respectively?
(a) Both deductive  (b) Reasoning by analogy, then inductive  (c) Both reasoning by analogy  (d) Inductive, then reasoning by analogy

Accepted Answer

The inspector moves from a set of specific observed instances (50 sampled items) to a general conclusion about the whole batch — the defining shape of inductive reasoning, with a probable but not certain conclusion. The colleague's argument instead draws a conclusion about one case (the new machine) based specifically on its noted resemblance to another, already-understood case (the older machine) — the defining shape of reasoning by analogy.

Answer: (d) Inductive, then reasoning by analogy. Trap (a) wrongly labels both as deductive, when neither argument offers a logically guaranteed conclusion. Trap (b) and trap (c) both misassign at least one of the two arguments to the wrong type — the inspector's argument is specific-to-general induction, not a resemblance-based analogy, and the colleague's argument is a resemblance-based analogy, not induction from a sample.

Practice — "Logical Reasoning"

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities