Syllogism Questions: 12 Practice Problems with Answers

Twelve original problems in the standard two-statements-one-conclusion format, sorted by the premise pattern that decides how to solve them. Each of the four sections opens with the rule that governs that pattern — and the trap built to catch you — then three questions with every answer explained.

A syllogism gives you two statements and asks what must follow. The statements are artificial on purpose — all retrievers are dogs, no freelancers are salaried — because the skill being tested is not knowledge of the world but whether you can keep 'must be true' separate from 'sounds true.' Nearly every wrong answer in this format is a statement that is plausibly true and simply not forced by the premises.

The format runs on a small number of rules. Two 'some' premises never conclude. Two negative premises never conclude. An 'All' statement never reverses. A conclusion needs the middle term fully covered by at least one premise. Conditionals allow the rule forward and its contrapositive — nothing else. The twelve questions below drill each rule in turn, so by the end you are solving on pattern recognition rather than intuition.

Syllogisms appear in logic courses, in aptitude and civil-service papers worldwide, and — dressed in conditionals — inside LSAT and GMAT reasoning questions. Work these twelve untimed with the explanations open; then, if you want the exam version of the same skill, the timed logical reasoning paper below runs twenty questions against a clock.

Prefer a scored, timed paper?

The 20-question logical reasoning test covers arguments, assumptions, and flaws in the same must-be-true spirit — 20 minutes on the clock, per-type accuracy report at the end.

Take the 20-minute timed test

The four premise patterns, with questions

Universal premises: All / No

3 questions

Universal premises draw the cleanest pictures: 'All A are B' puts circle A inside circle B; 'No A are B' pulls the circles apart. Chain two universals through a shared middle term and the conclusion reads straight off the diagram. The two errors to guard against: reversing an 'All' ('All retrievers are dogs' ≠ 'All dogs are retrievers'), and concluding something about a term the premises only excluded — being outside one circle pins down nothing else about you.

What the premises look like: "All A are B. All/No B are C." — two universal statements, then "which conclusion must be true?"

Question 1

Statements: All retrievers are dogs. All dogs are mammals.
Which conclusion must be true?

  1. AAll mammals are retrievers
  2. BAll retrievers are mammals
  3. CSome mammals are not dogs
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: B. All retrievers are mammals

🐱 Two 'All' statements that chain — retrievers sit inside dogs, dogs sit inside mammals — so the inner circle sits inside the outer one: all retrievers are mammals. (A) reverses the direction, the single most common syllogism error: 'All A are B' never flips into 'All B are A.' (C) feels true from general knowledge, but the premises don't establish it — there could, as far as these two statements know, be nothing in 'mammals' beyond dogs. Judge only what the premises force.

Question 2

Statements: All planets orbit a star. No comet is a planet.
Which conclusion must be true?

  1. ANo comet orbits a star
  2. BSome comets do not orbit stars
  3. CAll things that orbit stars are planets
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: D. No firm conclusion follows

🐱 Being excluded from the planet club says nothing about what comets do — orbiting stars might be open to non-planets too. (A) and (B) both assume that only planets orbit stars, which is (C), and (C) is the illicit reversal of premise one. This pattern — 'All A do X, B is not an A, so B doesn't do X' — is called denying the antecedent when written with conditionals, and it's wrong for the same reason here: the premises never said X was exclusive to A.

Question 3

Statements: No reptiles are warm-blooded. All lizards are reptiles.
Which conclusion must be true?

  1. ANo lizards are warm-blooded
  2. BSome lizards are warm-blooded
  3. CAll warm-blooded animals are lizards
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: A. No lizards are warm-blooded

🐱 Lizards sit entirely inside reptiles, and the reptile circle is entirely separated from the warm-blooded circle — so lizards can't touch warm-blooded either. This is one of the classic valid forms (logicians call it Celarent). Note what makes it work: the middle term 'reptiles' is fully covered by the 'No' premise. (B) contradicts the valid conclusion; (C) is an unrelated reversal.

Particular premises: Some

3 questions

'Some' means 'at least one — and nothing more.' Two rules do almost all the work in this family. First: two 'some' premises never produce a firm conclusion. Second: a conclusion needs the middle term fully covered ('distributed') by at least one premise — when both premises only partially touch the middle term, the two 'some' regions can live in separate corners and never meet. That second rule is the undistributed middle, the single most-missed trap in syllogism questions.

What the premises look like: "Some A are B…" — at least one premise starts with "Some".

Question 4

Statements: Some accountants run marathons. Everyone who runs marathons is disciplined.
Which conclusion must be true?

  1. ASome accountants are disciplined
  2. BAll accountants are disciplined
  3. CSome disciplined people are not accountants
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: A. Some accountants are disciplined

🐱 Take the accountants who run marathons — the premises guarantee at least one exists. Each of them is a marathon runner, and every marathon runner is disciplined, so those accountants are disciplined: some accountants are disciplined. (B) overreaches from 'some' to 'all.' (C) may sound safe, but nothing in the premises rules out a world where every disciplined person happens to be an accountant. A 'some' premise plus a covering 'all' premise is the standard recipe for a valid 'some' conclusion.

Question 5

Statements: Some novels are bestsellers. Some bestsellers are cookbooks.
Which conclusion must be true?

  1. ASome novels are cookbooks
  2. BSome cookbooks are novels
  3. CAll bestsellers are either novels or cookbooks
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: D. No firm conclusion follows

🐱 Two 'some' premises never yield a firm conclusion — that's a rule worth memorizing outright. The novels that are bestsellers and the cookbooks that are bestsellers may be entirely different corners of the bestseller list, and nothing forces them to overlap. (A) and (B) both assume the overlap. (C) invents a completeness claim no premise made. If both premises start with 'some,' the answer is 'nothing follows' every single time.

Question 6

Statements: All violinists are musicians. Some musicians are teachers.
Which conclusion must be true?

  1. ASome violinists are teachers
  2. BSome teachers are violinists
  3. CAll musicians are violinists
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: D. No firm conclusion follows

🐱 The trap here catches more people than any other syllogism pattern. The musicians who teach might all be pianists — nothing connects them to the violinist corner of the musician circle. For a conclusion to follow, the middle term (musicians) must be fully covered by at least one premise, and here neither premise covers all musicians: 'All violinists are musicians' covers all violinists, and 'Some musicians…' covers only some. Logicians call this the undistributed middle. (A) and (B) both fall for it; (C) is a reversal.

Negative premises: No / Some…are not

3 questions

Negative premises obey two bookkeeping rules: if a premise is negative, the conclusion must be negative; if both premises are negative, nothing follows. The productive patterns pin individuals down: a 'No' premise that fully covers the middle term bars a 'some' group from it (some designers are not salaried), and an 'All' rule read backwards — its contrapositive — disqualifies whoever lacks the guaranteed property (no badge, not a sponsor). Watch the direction of the 'All': espresso → coffee pins down espresso drinks, not coffee drinks.

What the premises look like: "No A are B" / "Some A are not B" — at least one premise denies something.

Question 7

Statements: No freelancers receive a salary. Some designers are freelancers.
Which conclusion must be true?

  1. ANo designers receive a salary
  2. BSome designers do not receive a salary
  3. CSome designers receive a salary
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: B. Some designers do not receive a salary

🐱 The designers who freelance — the premises guarantee they exist — are barred from salary by premise one. So some designers do not receive a salary. (A) overreaches: the non-freelancing designers may well be salaried. (C) is likely true in the real world but the premises don't force it, and 'must be true' is the only standard. One negative premise plus one particular premise, with the middle term fully covered by the 'No' statement, is a valid recipe (Ferio) — the conclusion is always a modest 'some…are not.'

Question 8

Statements: All conference sponsors received a gold badge. Some attendees did not receive a gold badge.
Which conclusion must be true?

  1. ASome attendees are not sponsors
  2. BNo attendees are sponsors
  3. CSome attendees are sponsors
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: A. Some attendees are not sponsors

🐱 Every sponsor has a badge, so anyone without a badge cannot be a sponsor. The badgeless attendees therefore aren't sponsors: some attendees are not sponsors. This is the contrapositive at work inside a syllogism (the valid form Baroco). (B) goes too far — the badged attendees might include sponsors. (C) is not forced: perhaps no attendee sponsors anything. When a premise says 'some…do not,' look for what the 'All' premise makes impossible for those individuals.

Question 9

Statements: All espresso drinks contain coffee. Some drinks that contain coffee are not served hot.
Which conclusion must be true?

  1. ASome espresso drinks are not served hot
  2. BAll espresso drinks are served hot
  3. CSome drinks served hot are not espresso drinks
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: D. No firm conclusion follows

🐱 Tempting — but the cold coffee drinks in premise two might all be iced lattes and cold brew, with not an espresso among them. Nothing forces the 'not hot' region to reach into the espresso circle, so (A) fails, and nothing establishes (B) or (C) either. Compare this with the sponsor question: there, the 'some…not' individuals were pinned down by the All-rule ('no badge → not a sponsor'). Here the All-rule runs the other way (espresso → coffee) and pins nothing. Direction is everything.

Conditional & either-or syllogisms

3 questions

Conditional syllogisms allow exactly two moves: apply the rule forward (A happened, so B) and take the contrapositive (B failed, so A didn't happen). The two forbidden moves are mirror images: affirming the consequent (B happened, so A) and denying the antecedent (A didn't happen, so B won't). Either/or statements add one more valid move — eliminate one side and the other must hold — but affirming a side proves nothing, since both sides of an 'or' may be true together.

What the premises look like: "If A, then B" / "Either A or B" — rules and alternatives instead of categories.

Question 10

Statements: If the museum waives its entry fee on a Sunday, attendance rises that day. Attendance did not rise this Sunday.
Which conclusion must be true?

  1. AThe museum did not waive its entry fee this Sunday
  2. BThe museum waived its entry fee this Sunday
  3. CAttendance never rises unless the fee is waived
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: A. The museum did not waive its entry fee this Sunday

🐱 The rule is waive → rise. This Sunday there was no rise; had the fee been waived, a rise was guaranteed — so the fee can't have been waived. Denying the consequent (modus tollens) is one of the two valid conditional moves. (C) reverses the rule into 'rise only if waived,' which was never stated: attendance might also rise for a blockbuster exhibition. Keep the arrow's direction sacred and take its contrapositive freely; anything else is invention.

Question 11

Statements: If it snows overnight, morning practice is cancelled. Morning practice was cancelled today.
Which conclusion must be true?

  1. AIt snowed overnight
  2. BIt did not snow overnight
  3. CPractice is cancelled only when it snows
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: D. No firm conclusion follows

🐱 Snow guarantees cancellation, but cancellation doesn't certify snow — the coach may be ill, the field flooded. Concluding (A) is affirming the consequent, the conditional twin of the syllogism reversal error: it treats 'snow is sufficient' as 'snow is necessary.' (B) is just as unforced, and (C) restates the same illegal reversal as a rule. When you're given rule + consequent-happened, the answer is 'nothing follows' — only rule + antecedent-happened, or rule + consequent-failed, yield conclusions.

Question 12

Statements: Either the shipment arrives today, or the production line pauses tomorrow. The production line will not pause tomorrow.
Which conclusion must be true?

  1. AThe shipment arrives today
  2. BThe shipment does not arrive today
  3. CThe production line paused yesterday
  4. DNo firm conclusion follows
▶Show answer & explanation

Answer: A. The shipment arrives today

🐱 An either/or claim promises at least one side holds. Strike out one side (no pause tomorrow) and the other side must hold: the shipment arrives today. This is the disjunctive syllogism, and it's watertight. The one care to take: eliminating a side is valid; affirming a side proves nothing about the other, because 'or' here may be inclusive — both could be true. If the statement had said the shipment arrives, you could not conclude the line won't pause.

Keep practicing

Necessary vs. sufficient conditions quizThe conditional section above in full: 12 questions on the two valid moves and the two classic errors.Logical reasoning test (20 questions, 20 minutes)Timed arguments — assumptions, flaws, inference — scored with a per-type report.GMAT critical reasoning questionsThe same deductive skeleton under exam conditions: twelve worked arguments across every GMAT question type, with the assumption made explicit each time.LSAT practice questions by typeWhere syllogistic skill gets applied to real arguments: ten five-option samples across the five LSAT question types.Logical reasoning questions, workedTwenty worked argument questions grouped into six types, each with a field guide.

Syllogism questions — FAQ

What is a syllogism, with an example?

A syllogism is a two-premise argument in which a conclusion follows from a shared middle term. The textbook example: all men are mortal; Socrates is a man; therefore Socrates is mortal. 'Man' is the middle term that links the other two and disappears from the conclusion.

How do I solve syllogism questions quickly?

Draw or imagine circles: 'All A are B' nests A inside B, 'No A are B' separates the circles, 'Some A are B' overlaps them with an X in the overlap. Then check only whether each option is forced by the picture. With practice the rules replace the drawing: some+some and negative+negative never conclude, 'All' never reverses, and the middle term must be fully covered once.

What is the undistributed middle fallacy?

A conclusion is only valid if the middle term — the one appearing in both premises — is fully covered by at least one of them. 'All violinists are musicians; some musicians are teachers' leaves 'musicians' only partially touched by each premise, so the violinists and the teachers may never overlap. Concluding that they do is the undistributed middle fallacy, the most common error in this format.

Which exams use syllogism questions?

Directly: logic and philosophy courses, and reasoning sections of banking, civil-service and aptitude papers in many countries. Indirectly: LSAT Logical Reasoning and GMAT Critical Reasoning test the same machinery through conditional statements — 'only if,' 'unless,' contrapositives — wrapped in realistic arguments.

Are these questions free, and are they real exam questions?

Free, no sign-up, explanations open on the page. All twelve are original questions written for this page — not recycled from any exam — checked against the classical rules of the valid syllogistic forms.