# Syllogism Questions with Answers — Venn Diagram Method

> Syllogism reasoning questions with answers using the Venn diagram method. All, some and no statements with conclusions explained step by step.

Source: https://www.sansal.in/aptitude/syllogism · Last updated: 2026-09-19 · How often it appears: High. Usually a set of 3-5 questions sharing one instruction block.

Syllogism is the topic where intuition is most likely to be wrong, because the questions are designed around the gap between what follows logically and what sounds reasonable. The Venn diagram method removes the guesswork entirely.

## Concepts

### Treat the statements as true, however absurd

The instruction always says to take the given statements as true even if they contradict common knowledge. "All chairs are tables" is fine. Bringing in real-world knowledge is the single biggest cause of wrong answers in this topic.

### A conclusion must hold in every possible diagram

Draw the Venn diagram. If there is even one valid way to draw the circles where the conclusion fails, the conclusion does not follow. "Might be true" is not "follows". This is the whole test.

### What each statement type allows

"All A are B" puts circle A entirely inside B. "No A are B" makes the circles disjoint. "Some A are B" means they overlap — and critically, it does NOT rule out that all A are B. "Some A are not B" means at least one A sits outside B.

### The either-or case

When two conclusions individually fail but between them cover every possibility, and they cannot both be true at once, the answer is "either I or II follows". This typically arises with a "some" and a "no" pair on the same two terms.

## Formulas

| Formula | Rule | Note |
| --- | --- | --- |
| All A are B | Circle A lies entirely inside circle B |  |
| No A are B | Circles A and B do not touch |  |
| Some A are B | Circles A and B overlap | Does not exclude the possibility that all A are B. |
| Some A are not B | Part of A lies outside B |  |
| Valid chain | All A are B + All B are C → All A are C |  |
| Invalid reversal | All A are B does NOT give All B are A |  |

## Worked examples

### Example 1

**Question:** Statements: All roses are flowers. All flowers are plants. Conclusions: (I) All roses are plants. (II) All plants are roses.

**Solution:**

1. Draw: roses inside flowers, flowers inside plants. So roses sit inside plants.
2. Conclusion I: every rose is inside the plants circle, in every possible drawing. It follows.
3. Conclusion II: the plants circle is the largest and may contain much that is not a rose. It does not follow.

**Answer:** Only conclusion I follows

### Example 2

**Question:** Statements: Some pens are books. All books are papers. Conclusions: (I) Some pens are papers. (II) All pens are papers.

**Solution:**

1. Some pens are books, so there is an overlap region between pens and books.
2. All books sit inside papers, so that overlap region is inside papers too.
3. Conclusion I: the pens in that overlap are papers, so some pens are papers. It follows.
4. Conclusion II: the rest of the pens circle can be drawn entirely outside papers. It does not follow.

**Answer:** Only conclusion I follows

### Example 3

**Question:** Statements: All cats are dogs. No dogs are birds. Conclusions: (I) No cats are birds. (II) Some dogs are cats.

**Solution:**

1. Cats sit entirely inside dogs. The dogs circle does not touch birds at all.
2. Conclusion I: since every cat is inside dogs, and dogs never meet birds, no cat can be a bird. It follows.
3. Conclusion II: all cats are dogs and the cats circle is non-empty, so there are dogs that are cats. It follows.

**Answer:** Both conclusions follow

## Practice questions

1. Statements: All books are pens. All pens are pencils. Conclusion: All books are pencils.
   - A. Follows
   - B. Does not follow
   - C. Either follows
   - D. Cannot be determined
   - **Answer:** A. Follows — A valid chain: books inside pens inside pencils, so books are inside pencils in every drawing.

2. Statements: All dogs are animals. Conclusion: All animals are dogs.
   - A. Follows
   - B. Does not follow
   - C. Either follows
   - D. Both follow
   - **Answer:** B. Does not follow — Reversing an "all" statement is invalid. The animals circle can contain much more than dogs.

3. Statements: Some apples are fruits. Conclusion: Some fruits are apples.
   - A. Follows
   - B. Does not follow
   - C. Either follows
   - D. Cannot be determined
   - **Answer:** A. Follows — "Some" is symmetric: an overlap between apples and fruits is the same overlap read the other way.

4. Statements: No cats are dogs. Conclusion: No dogs are cats.
   - A. Follows
   - B. Does not follow
   - C. Either follows
   - D. Cannot be determined
   - **Answer:** A. Follows — "No" is symmetric too — disjoint circles are disjoint whichever one you name first.

5. Statements: All pens are books. Some books are papers. Conclusion: Some pens are papers.
   - A. Follows
   - B. Does not follow
   - C. Either follows
   - D. Both follow
   - **Answer:** B. Does not follow — The books that overlap papers need not be the ones that are pens. You can draw the pens circle entirely clear of papers, so it does not follow.

6. In syllogism, the statement "Some A are B" also allows the possibility that:
   - A. No A are B
   - B. All A are B
   - C. A and B are unrelated
   - D. B does not exist
   - **Answer:** B. All A are B — "Some" guarantees at least one overlap but sets no upper bound, so the case where all A are B is still permitted.

## Where marks get lost

- Using real-world knowledge instead of taking the statements as given.
- Reversing an "all" statement — All A are B does not give All B are A.
- Accepting a conclusion that is merely possible rather than necessary.
- Treating "some" as if it excluded "all".

## Related topics

- [Blood Relations](https://www.sansal.in/aptitude/blood-relations)
- [Number & Alphabet Series](https://www.sansal.in/aptitude/series)
- [Coding–Decoding](https://www.sansal.in/aptitude/coding-decoding)

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