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Syllogism Questions with Solutions

Syllogism questions test pure logic, not real-world knowledge — you have to accept the given statements as true even when they sound absurd, and judge only whether each conclusion is logically forced. Here’s the approach, four fully worked examples covering the patterns that trip people up most, and a few to try yourself.

The approach, quickly

  • Treat every statement as 100% true, no matter how odd it sounds ("All cats are dogs" is a valid statement for this question) — judge conclusions purely on logic, not on what you know about the real world.
  • Four statement types matter: "All A are B", "No A are B", "Some A are B", and "Some A are not B".
  • "Some A are B" can always be flipped to "Some B are A" — this conversion is always valid. But "All A are B" can NOT be flipped to "All B are A" — that is a classic trap. "All A are B" can only be weakened to "Some B are A" (these questions assume A has at least one member).
  • Sketch a quick Venn diagram for each conclusion and check whether it holds in every possible arrangement of the circles, not just the most obvious one. If you can draw even one valid arrangement where the conclusion is false, it does not follow.

Worked examples

1. Statements: All cats are dogs. All dogs are cows. Conclusions: I. All cats are cows. II. All cows are cats. Which conclusion(s) logically follow?

Solution

  1. All cats are dogs means the "cats" circle sits entirely inside the "dogs" circle. All dogs are cows means the "dogs" circle sits entirely inside the "cows" circle.
  2. So the "cats" circle is entirely inside the "cows" circle too — Conclusion I is forced in every possible arrangement.
  3. Conclusion II is not forced — the "cows" circle could easily be much bigger, containing cows that are neither dogs nor cats. It does not follow.

Answer: Only Conclusion I follows

2. Statements: Some pens are books. All books are tables. Conclusions: I. Some pens are tables. II. Some tables are pens. Which conclusion(s) logically follow?

Solution

  1. Some pens are books means the "pens" circle and "books" circle overlap. All books are tables means the "books" circle sits entirely inside the "tables" circle.
  2. The pens that overlap with books are therefore also inside tables — so some pens are tables. Conclusion I is forced.
  3. "Some pens are tables" (just shown true) can always be flipped to "Some tables are pens" — this flip is always valid for "Some…are" statements. So Conclusion II follows too.

Answer: Both conclusions follow

3. Statements: No apples are oranges. Some oranges are fruits. Conclusions: I. Some fruits are not apples. II. No apples are fruits. Which conclusion(s) logically follow?

Solution

  1. No apples are oranges means the "apples" circle and "oranges" circle do not overlap at all.
  2. Some oranges are fruits means part of the "oranges" circle overlaps with the "fruits" circle — and that overlapping part, being entirely within oranges, cannot contain any apples (since apples and oranges never overlap).
  3. So those particular fruits (the ones that are oranges) are definitely not apples — "Some fruits are not apples" is forced. Conclusion I follows.
  4. "No apples are fruits" is not forced — apples could still overlap with fruits through some path that has nothing to do with oranges; nothing in the statements rules that out. Conclusion II does not follow.

Answer: Only Conclusion I follows

4. Statements: All books are pens. No pen is a pencil. Conclusions: I. No book is a pencil. II. Some pens are books. Which conclusion(s) logically follow?

Solution

  1. All books are pens means the "books" circle sits entirely inside the "pens" circle. No pen is a pencil means the "pens" circle and "pencils" circle do not overlap at all.
  2. Since the "books" circle is entirely inside the "pens" circle, and the "pens" circle never touches the "pencils" circle, the "books" circle can’t touch the "pencils" circle either — "No book is a pencil" is forced. Conclusion I follows.
  3. "All books are pens" guarantees every book is a pen, and since books exist, at least some pens are books — "Some pens are books" is forced. Conclusion II follows.

Answer: Both conclusions follow

Try these yourself

Sketch the Venn diagram step by step, then check against the answer.

1. Statements: All mobiles are laptops. Some laptops are tablets. Conclusions: I. Some mobiles are tablets. II. Some tablets are mobiles. Which conclusion(s) follow?

Answer: Neither conclusion follows (the "some laptops are tablets" overlap need not touch mobiles at all)

2. Statements: Some doctors are engineers. No engineer is a teacher. Conclusions: I. Some doctors are not teachers. II. No doctor is a teacher. Which conclusion(s) follow?

Answer: Only Conclusion I follows

3. Statements: All squares are rectangles. All rectangles are polygons. Conclusions: I. All squares are polygons. II. Some polygons are squares. Which conclusion(s) follow?

Answer: Both conclusions follow

Where this comes up

Syllogism is a regular topic in the Reasoning/General Intelligence section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and tends to carry extra weight in banking exams specifically.

Practice more Syllogism questions

This page covers the approach and a handful of worked examples. Pariksha Saathi has full topic-wise practice sets for Syllogism (and every other Reasoning/Quant/English topic) with instant scoring and explanations — free, no account required.

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