Syllogism Questions: Venn Method and Solved Examples

The Four Statement Types

Types of Conclusions

Definite

Must be true in every possible diagram. "Some pens are bags."

Possibility

Could be true in at least one diagram without breaking any statement. "All pens being bags is a possibility."

Either-or pair

Two conclusions about the same two groups where neither is certain, but exactly one must be true, such as "Some A are B" and "No A is B".

The Venn Diagram Method

1. 1

   Draw the least overlap first

   Draw each statement with the smallest overlap it allows. "Some A are B" gets a small overlap, not a full one.

2. 2

   Check each definite conclusion

   If it is false in this diagram, it does not follow. If it is true, check that no other allowed diagram makes it false before you mark it as following.

3. 3

   Redraw for possibility conclusions

   Try to make the conclusion true by moving circles, without breaking any statement. If you can, the possibility follows.

4. 4

   Look for an either-or pair

   If two conclusions fail on their own but one of them must be true, the answer is "either I or II follows".

Worked Practice Questions

Original questions written for this page. Try each before reading the solution.

1. 1

   Practice question 1: Statements: All pens are books. All books are bags. Conclusions: I. All pens are bags. II. Some bags are pens.

   Pens sit inside books, and books sit inside bags, so pens sit inside bags. Conclusion I follows. All pens are bags, so reversing gives some bags are pens. Conclusion II follows. Answer: both follow.

2. 2

   Practice question 2: Statements: Some cups are plates. No plate is a spoon. Conclusions: I. Some cups are not spoons. II. No cup is a spoon.

   The cups that are plates cannot be spoons, so at least some cups are not spoons. Conclusion I follows. Other cups lie outside the plate circle and could still be spoons, so II is not certain. Answer: only I follows.

3. 3

   Practice question 3: Statements: All roses are flowers. No flower is a tree. Conclusions: I. No rose is a tree. II. Some trees are roses.

   Roses sit inside flowers, and flowers do not touch trees. So roses cannot touch trees either. Conclusion I follows, and II contradicts it. Answer: only I follows.

4. 4

   Practice question 4: Statements: Some boxes are tins. All tins are jars. Conclusions: I. Some jars are boxes. II. All boxes being jars is a possibility.

   The boxes that are tins are also jars, so some boxes are jars, and reversing gives some jars are boxes. I follows. Nothing stops the rest of the boxes from sitting inside jars too, so II is possible. Answer: both follow.

5. 5

   Practice question 5: Statements: Some keys are locks. Some locks are doors. Conclusions: I. Some keys are doors. II. No key is a door.

   Two "some" statements give no definite link between keys and doors. Draw it both ways: keys can overlap doors, or keep away from them. So neither I nor II is certain alone. But they are about the same two groups and exactly one must be true. Answer: either I or II follows.

Common Traps

• check_circleReversing "All A are B" as "All B are A". It only gives "Some B are A".
• check_circleReversing "Some A are not B". It has no valid reverse at all.
• check_circleUsing real-world knowledge. If the statement says all roses are trees, treat it as true for the question.
• check_circleDrawing too much overlap. "Some A are B" does not mean most or all. Start with the smallest overlap.
• check_circleMarking a possibility as true when a definite conclusion rules it out. In practice question 3, "Some roses being trees is a possibility" would not follow.
• check_circleMarking "either-or" for any two failed conclusions. It applies only when the two are about the same groups and one of them must be true.

How Bank and SSC Papers Test This

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