In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusion(s) logically follows/follow from the statements. Statements: Some shirts are pants. All pants are jackets. All jackets are trousers. Conclusions: I. Some trousers are shirts. II. All jackets are shirts.
- (a)Only conclusion I follows.
- (b)Only conclusion II follows.
- (c)Both conclusions I and II follow.
- (d)Neither conclusion I nor II follows.
Answer
Why
Correct — A. Rule: a chain of All statements carries a Some forward through it, but nothing travels back up the chain.
Some shirts are pants. All pants are jackets, so those same shirts are jackets.
All jackets are trousers, so those same shirts are trousers too. Some trousers are shirts is therefore forced, and conclusion I follows.
Conclusion II runs the chain backwards. All jackets are shirts would need every jacket to be a shirt, but shirts entered only through some shirts being pants, so jackets need not be shirts at all.
One conclusion follows and the other does not, which is option (a).
Why the others are wrong
- (b)Only conclusion II follows. — It keeps the conclusion that fails and drops the one that holds. All jackets are shirts reverses an All statement, which the premises never license.
- (c)Both conclusions I and II follow. — Accepting both requires All jackets are shirts to follow. It does not, because nothing forces any jacket outside the shirts-that-are-pants group to be a shirt.
- (d)Neither conclusion I nor II follows. — This discards conclusion I, which does follow. The shirts that are pants are jackets, and all jackets are trousers, so some trousers are shirts is guaranteed.
Concept
Three statements linked by All build a one-way road. Some shirts are pants places part of shirts inside pants; All pants are jackets carries that part into jackets; All jackets are trousers carries it into trousers.
What travels along the road is existence, not universality. A Some entering at the start survives to the end, so a Some conclusion between the two ends is safe.
What never travels is the reverse direction. All jackets are trousers gives nothing about all trousers, and it gives nothing about jackets being shirts.
Conclusion II is not false. Nothing in the statements forbids every jacket from being a shirt — it simply is not forced, and a syllogism asks only what must follow.
Key facts
- A Some statement converts: Some shirts are pants gives Some pants are shirts.
- All statements chain: All pants are jackets with All jackets are trousers gives All pants are trousers.
- An All statement does not convert, so All jackets are trousers gives nothing about all trousers.
- Conclusion I holds because the shirts that are pants must also be trousers.
Study next
Common traps
- Reversing an All statement to reach a universal conclusion
- Rejecting conclusion I because shirts and trousers never appear in one statement together
- Treating the three statements as separate pairs instead of one chain
The two conclusions are tested independently against the premises, so a conclusion that fails says nothing about the other. Work each one to a verdict before reading the option list, since the options are only combinations of those two verdicts.
Related PYQs
No directly related past PYQ was found.