All flowers are toys. Some toys are trees. Some butterflies are trees, then A.…
2020
All flowers are toys. Some toys are trees. Some butterflies are trees, then
A. No butterfly is flower
B. Some butterflies are toys
C. Some toys are flowers
D. Some trees are flowers
E. Some trees are butterflies
Choose the correct answer from the options given below:
- A.
A and B only
- B.
C and E only
- C.
B and E only
- D.
B and D only
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept: A universal statement “All A are B” converts only by limitation to “Some B are A” (never to “All B are A”). A particular statement “Some A are B” converts simply to “Some B are A”, and this holds with full certainty. When a term that links two statements is particular (“some”) in both of them, that term is undistributed in each, so no valid conclusion can be drawn connecting the other two end terms.
Conclusion A (No butterfly is flower): the only path between butterflies and flowers runs through “trees”, but “Some toys are trees” and “Some butterflies are trees” are both particular statements sharing that middle term — it is undistributed in both, so nothing about butterflies and flowers can be validly fixed. Does not follow.
Conclusion B (Some butterflies are toys): for the same reason — two particular premises sharing the undistributed middle term “trees” — no valid link between butterflies and toys can be drawn. Does not follow.
Conclusion C (Some toys are flowers): “All flowers are toys” converts by limitation directly to “Some toys are flowers”. Follows.
Conclusion D (Some trees are flowers): no premise relates trees and flowers directly, and the toys–trees and flowers–toys relations cannot be chained to fix any trees–flowers overlap. Does not follow.
Conclusion E (Some trees are butterflies): a particular statement converts simply, so “Some butterflies are trees” gives “Some trees are butterflies” directly. Follows.
Cross-check: draw flowers entirely inside toys, with toys and trees overlapping in one region and butterflies and trees overlapping in another (possibly different) region — this diagram satisfies every statement. It directly shows the toys–flowers overlap and the trees–butterflies overlap, while the butterflies–flowers and trees–flowers relations stay undetermined, exactly matching the conclusions above.
So only conclusions C and E necessarily follow — the correct choice is “C and E only”.