Quick Summary: Logical Deduction and Induction gives 1 to 3 marks in GATE General Aptitude 2027 in every paper (DA, RA, CS, ME, EE, CE, EC). Deduction questions come as syllogisms (all, some, no), if-then statements and “which conclusion follows” sets. Induction questions come as arguments to strengthen or weaken, assumptions and inferences from data. This guide gives you the Venn-diagram method for syllogisms, the contrapositive rule for conditionals, the truth-teller and liar method, 8 solved previous-year and GATE-style questions, a 5-question practice set, a one-page rule sheet and the traps that convert a sure mark into negative marking.
📋 Table of Contents
- Why this topic matters in GATE GA
- What the official GA syllabus says
- Deduction versus induction: the one distinction GATE tests
- Syllogisms with Venn diagrams
- If-then statements and the contrapositive
- Truth-tellers, liars and consistency puzzles
- Induction: assumptions, strengthen and weaken
- Shortcuts and traps
- Solved PYQs and GATE-style questions
- Practice set
- One-page rule sheet
- Common mistakes
- FAQs
Why this topic matters in GATE GA
Logic questions are the purest aptitude questions in GATE. There is no formula to recall and no arithmetic to slip on. You are given two or three statements and asked which conclusion must follow. Since GA became a standard 15-mark section in 2010, at least one such question has appeared almost every year, and since the 2021 syllabus revision (“Analytical Aptitude: Logic: deduction and induction”) it is an explicitly named topic.
The reason students lose this mark is not difficulty. It is that they answer from common sense instead of from the statements. “All hill-stations have a lake” does not say anything about places with two lakes, but a tired brain at the end of a three-hour paper will invent that rule. This chapter trains you to read only what is written, and to check every option against a diagram or a case table before you click.
Here is roughly how much the topic has contributed. Candidates targeting 15/15 in GA should settle any logic question in 60 to 90 seconds.
| Year | Marks from this topic (approximate, across papers) | Typical question type |
|---|---|---|
| 2019 | 1 to 2 | Two statements, which conclusion follows |
| 2020 | 1 to 2 | Inference from a short passage |
| 2021 | 1 to 3 | Syllogism with two “All” statements |
| 2022 | 1 to 3 | Statements that cannot be true together |
| 2023 | 1 to 2 | If-then statement, valid conclusion |
| 2024 | 1 to 2 | Truth-teller and liar puzzle |
| 2025 | 1 to 3 | Argument to weaken, assumption |
| 2026 | 1 to 2 | Syllogism with “some” and “no” |
What the official GA syllabus says
This post covers the first item, “Logic: deduction and induction”. Analogy and numerical relations are the next post in the series. The complete GA syllabus and weightage are in the GATE General Aptitude 2027 hub, and the previous post covered Speed-Time-Distance, Work-Time, Clocks and Calendars.
Deduction versus induction: the one distinction GATE tests
Deduction goes from general rules to a particular case, and if the premises are true the conclusion is guaranteed. “All metals conduct electricity. Copper is a metal. Therefore copper conducts electricity.” There is no escape from that conclusion.
Induction goes from particular observations to a general rule, and the conclusion is only probable. “Every swan I have seen is white. Therefore all swans are white.” A single black swan breaks it. GATE tests induction by asking which option strengthens or weakens such an argument, or which unstated assumption it depends on.
The exam phrase that tells you which mode you are in: “which of the following can be logically inferred” or “must be true” means deduction (prove it or reject it). “Which option most strengthens / weakens” or “the argument assumes” means induction (judge the support, not certainty).
Solution: The rule is “above 90 implies cleared”. Meera satisfies the condition, so the conclusion applies to her. (A) adds “top”, which is not in the rule. (C) is the inverse of the rule, which does not follow. (D) is outside the statements.
Answer: (B) Meera cleared GATE.
Syllogisms with Venn diagrams
A syllogism has two premises and asks which conclusion follows. The four statement types are:
- All A are B (universal positive): circle A sits inside circle B.
- No A is B (universal negative): circles A and B do not touch.
- Some A are B (particular positive): circles A and B overlap, and the overlap is non-empty.
- Some A are not B (particular negative): part of A lies outside B.
The test for a conclusion is simple: a conclusion follows only if it is true in every diagram consistent with the premises. If you can draw even one legal diagram where the conclusion fails, reject it. GATE options are built from exactly this: the wrong options are true in the “obvious” diagram but false in a less obvious one.
The results worth memorising (A, B, C are the three terms):
| Premises | Valid conclusion | Tempting but invalid |
|---|---|---|
| All A are B. All B are C. | All A are C. Some C are A. | All C are A. |
| Some A are B. All B are C. | Some A are C. Some C are A. | All A are C. |
| All A are B. Some B are C. | Nothing about A and C. | Some A are C. |
| All A are B. No B is C. | No A is C. | Some A are C. |
| Some A are B. No B is C. | Some A are not C. | No A is C. |
| All A are C. All B are C. | Nothing about A and B. | Some A are B. |
| Some A are not B. | Nothing about B alone. | Some B are not A. |
Two conversion rules you may use freely: “Some A are B” converts to “Some B are A”, and “No A is B” converts to “No B is A”. “All A are B” converts only to “Some B are A” (never to “All B are A”), and “Some A are not B” does not convert at all.
Solution: Draw robots inside machines. The “expensive” circle must overlap machines, but it can overlap only the part of machines outside robots. So I is not forced. II is just the conversion of “Some machines are expensive”, so it always holds.
Answer: Only II follows.
Solution: Cameras sit inside sensors; sensors and cheap do not touch. So cameras and cheap cannot touch either.
Answer: (B) No camera is cheap.
If-then statements and the contrapositive
A conditional “If P then Q” has four relatives, and only one of them is equivalent to it:
| Name | Form | Follows from “If P then Q”? |
|---|---|---|
| Original | If P then Q | Given |
| Converse | If Q then P | No |
| Inverse | If not P then not Q | No |
| Contrapositive | If not Q then not P | Yes, always |
So from “If it rains, the match is cancelled” you may conclude “The match was not cancelled, so it did not rain” (contrapositive). You may not conclude “The match was cancelled, so it rained” (converse): a wet pitch or a power cut could also cancel it.
Two other phrasings GATE uses: “P only if Q” means “If P then Q” (Q is necessary for P). “P if and only if Q” means both directions. “Unless Q, not P” also means “If P then Q”. Translate every statement into “If … then …” form before you touch the options.
Solution: “P only if Q” is “If shortlisted then valid score”. Its contrapositive is “If no valid score then not shortlisted”, which is (B). (A) and (D) are the converse. (C) contradicts the statement.
Answer: (B).
Truth-tellers, liars and consistency puzzles
These puzzles give you a few people who always tell the truth or always lie, and their statements. The method is assume and check: assume one person is truthful, propagate the consequences, and see whether every statement stays consistent. If you hit a contradiction, the assumption was wrong. With three people you never need more than two or three cases.
A second family is “exactly one of these statements is true” (or exactly two). Here you take each possible fact (the prize is in box 1, box 2, box 3) in turn, count how many statements become true, and keep the case that matches the given count.
Solution: Case 1: A truthful. Then B is a liar, so B’s statement is false, so A and B are of the same type. But they are different (A truthful, B liar). Contradiction. Case 2: A a liar. Then B is truthful, so B’s statement is true: A and B are of different types. A liar, B truthful: different. Consistent.
Answer: A is a liar and B is a truth-teller.
Induction: assumptions, strengthen and weaken
An inductive argument has evidence and a conclusion, with a gap between them. The assumption is the unstated bridge across that gap. A strengthener is new information that makes the bridge sturdier; a weakener attacks it. The fastest test for an assumption is the negation test: negate the option, and if the argument collapses, that option was the assumption.
Three recurring gaps in GATE arguments:
- Correlation to causation: “Cities with more cafes have higher incomes, so opening cafes raises income.” Weaken by giving reverse causation or a third factor.
- Sample to population: “All five toppers I know used book X, so book X is the best.” Weaken by showing the sample is unrepresentative.
- Sufficient to necessary: “Every topper attended coaching, so coaching is necessary.” Weaken by producing a topper who did not attend; the fact that many coached students failed does not weaken it (it attacks sufficiency, not necessity).
Solution: The gap is correlation to causation. (B) offers reverse causation: good preparation causes both the sleep and the score. (A) only says the effect is not universal, which averages already allow. (C) and (D) are neutral or strengthening.
Answer: (B).
Shortcuts and traps
❌ Treating “Some A are B” as implying “Some A are not B”. It does not; all A may be B.
❌ Accepting the converse: “If P then Q, and Q is true, so P is true.”
❌ Using real-world knowledge (“Ooty is obviously a hill-station”) instead of the given statements.
❌ In liar puzzles, forgetting to verify that the final assignment makes every statement consistent, not just the first one.
❌ Confusing “weakens” with “proves false”. A weakener only reduces support.
❌ Picking an option that attacks sufficiency when the argument claims necessity, or vice versa.
Solved previous-year and GATE-style questions
Years are given only where I am confident the question appeared; the rest are built to the same pattern. Many more are solved in the PiyushAI Aptitude Test Series with video explanations.
Solution: Professors sit inside researchers. Scientists overlap professors, so the overlapping scientists are also researchers. Hence some scientists are researchers, which converts to some researchers are scientists. (A) over-reaches, (B) reverses the second premise, (D) contradicts.
Answer: (C).
Solution: “Has a lake” means at least one lake; two lakes satisfies it. So Ooty may or may not be a hill-station, and (i) is not forced. The premise says nothing about an upper limit, so (ii) is not forced either.
Answer: (D) neither.
Solution: Both circles sit inside “microorganisms” but nothing links them. They may overlap (so II fails) or be disjoint (so I fails). Neither is forced.
Answer: Neither I nor II.
Solution: The singers who are poets (at least one exists) cannot be engineers, so I is forced. Singers who are not poets could be engineers, so II is not forced.
Answer: (A) Only I.
Solution: Ravi satisfies Q (studied daily), not P. Affirming Q tells us nothing about P (that would be the converse). So nothing can be concluded.
Answer: (C).
Solution: (A) is the converse, (C) is the inverse, (D) is unsupported. (B) is the contrapositive.
Answer: (B).
Solution: Suppose R is truthful. Then P and Q are both liars. But P (a liar) says Q is a liar, which would then be true, a contradiction. So R lies, meaning P and Q are not both liars. Q says R is a liar, which is true, so Q is truthful. P says Q is a liar, which is false, so P lies. Check: P lies, Q truthful, R lies, and R’s claim “both P and Q lie” is indeed false. Consistent.
Answer: Only Q tells the truth.
Solution: Prize in A: labels A true, B true, C false (two true). Prize in B: A false, B false, C true (one true). Prize in C: A false, B true, C true (two true). Only the second case gives exactly one true label.
Answer: Box B.
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Best GATE Aptitude Test Series 2027
General Aptitude is 15 marks in every GATE paper and the easiest 15 marks to lose to silly mistakes. The PiyushAI Aptitude Test Series by Piyush Wairale (IIT Madras) gives you topic-wise tests on exactly this chapter, full-length GA mocks in the real GATE interface, detailed video and text solutions, and All-India rank analysis.
Practice set
Attempt these in 7 minutes before opening the key.
- Statements: All drones are aircraft. No aircraft is a submarine. Which conclusion must be true? (A) Some submarines are drones (B) No drone is a submarine (C) Some drones are submarines (D) All submarines are aircraft
- Statements: Some keys are locks. All locks are doors. Which conclusion must be true? (A) All keys are doors (B) Some keys are doors (C) No key is a door (D) All doors are locks
- “If n is even then n2 is even.” It is known that n2 is odd. Which follows? (A) n is even (B) n is odd (C) n may be even or odd (D) n2 is even
- Rohit says “Exactly one of us two is lying.” Sita says “Rohit is lying.” Each person either always lies or always tells the truth. Who is lying? (A) Rohit only (B) Sita only (C) Both (D) Neither
- “Cities with more trees report lower summer temperatures. Therefore planting trees will cool Amravati.” Which option most strengthens the argument? (A) In a controlled study, shaded streets were 3°C cooler than unshaded streets in the same city (B) Amravati has fewer trees than Nagpur (C) Trees need regular watering (D) Hot cities tend to have fewer parks
Show answer key
- (B). Drones sit inside aircraft; aircraft and submarines are disjoint; so drones and submarines are disjoint.
- (B). The keys that are locks are also doors, so some keys are doors. “All keys are doors” is not forced.
- (B). Contrapositive: if n2 is not even then n is not even, so n is odd.
- (B). If Rohit is truthful, exactly one lies, so Sita lies, and her claim “Rohit is lying” is indeed false. Consistent. If Rohit lies, Sita’s claim is true so Sita is truthful, which makes exactly one liar (Rohit), making Rohit’s statement true, a contradiction.
- (A). A controlled comparison within one city removes the “different cities differ in other ways” objection and supports the causal link. (B) and (D) restate correlation; (C) is irrelevant.
One-page rule sheet
2. A conclusion follows only if it holds in every diagram consistent with the premises.
3. All A are B + All B are C gives All A are C. Some A are B + All B are C gives Some A are C.
4. All A are B + No B is C gives No A is C. Some A are B + No B is C gives Some A are not C.
5. Two “Some” premises, two negative premises, or two “All” premises sharing only the predicate give no conclusion.
6. Conversions: Some A are B = Some B are A. No A is B = No B is A. All A are B gives only Some B are A.
7. “If P then Q” is equivalent only to its contrapositive “If not Q then not P”. Converse and inverse do not follow.
8. “P only if Q” and “Unless Q, not P” both mean “If P then Q”. “P if and only if Q” means both directions.
9. Liar puzzles: assume one speaker truthful, propagate, check every statement; switch case on contradiction.
10. “Exactly k statements are true”: test each possible fact and count the true statements.
11. Assumption test: negate the option; if the argument collapses, that is the assumption.
12. Weaken a necessity claim with a counterexample that lacks the condition; weaken a causal claim with reverse causation or a third factor.
Common mistakes
❌ Treating “All A are B” as symmetric.
❌ Concluding “Some A are C” from “All A are B” and “Some B are C”.
❌ Accepting the converse or inverse of a conditional as a valid inference.
❌ Reading “some” as “some but not all”.
❌ Stopping a liar puzzle at the first consistent-looking case without checking the remaining statements.
❌ Spending three minutes on one logic question; if two readings have not settled it, mark for review and return later.
FAQs
How many logic questions appear in GATE General Aptitude?
Typically 1 question of 1 or 2 marks per paper, occasionally 2 questions. Since 2021 the topic is named explicitly in the syllabus, so expect at least one every year.
Should I learn formal rules of syllogism or just draw Venn diagrams?
Venn diagrams are enough for GATE. The exam never uses more than three terms. Draw the stingiest diagram the premises allow and test each option against it.
What is the difference between inference and assumption questions?
An inference is something that must be true given the statements (deduction). An assumption is something the argument needs but does not state (induction). Use the negation test for assumptions.
Is the PiyushAI Aptitude Test Series enough for GA?
Yes. The Best GATE Aptitude Test Series 2027 has a dedicated logical reasoning test, tests on every other GA chapter, full-length GA mocks in the GATE interface, solved PYQs from 2010 to 2026 and All-India rank analysis. With the free guides on this site it covers the whole GA section.
Are logic questions the same for GATE DA, RA, CS and ME?
Yes. The GA section is common to all papers, so the same types of syllogisms, conditionals and argument questions appear for every branch.
Stop losing easy marks. Practise this topic under exam pressure.
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Related guides: GATE General Aptitude 2027 hub | All GATE General Aptitude articles | GATE DA Syllabus 2027 | GATE RA Syllabus 2027
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