Question

In each of the questions below, two statements are given followed by two conclusions numbered I and II. Consider the two given statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions logically follow(s) from the statements.

Statements: All bulbs are birds. Some birds are butterflies.
Conclusions:
I. All butterflies are bulbs.
II. Some bulbs are butterflies.

• A. if only conclusion II follows
• B. if only conclusion I follows
• C. if either conclusion I or II follows
• D. if neither conclusion I nor II follows

Hint:

Test the syllogism with a Venn diagram - watch for the undistributed middle term "birds".

Answer 1

The Correct Option is D

A second way to confirm this is to construct one valid arrangement of numbers that satisfies both statements but makes each conclusion false, since a single valid counter-example is enough to show a conclusion does not necessarily follow.

1. Let birds total 100. Let bulbs be a small group of, say, 10 birds, so "all bulbs are birds" holds since $10 \le 100$.
2. Let "some birds are butterflies" be satisfied by 20 birds overlapping with butterflies, and choose these 20 birds to be entirely separate from the 10 bulbs, which is allowed since the statement never says the overlap must include the bulbs.
3. Check Conclusion I: are all butterflies bulbs? Butterflies overlap with 20 birds, none of which are bulbs, so butterflies are not bulbs at all in this arrangement. Conclusion I fails.
4. Check Conclusion II: are some bulbs butterflies? The 10 bulbs and the 20 birds that are butterflies do not overlap in this arrangement, so zero bulbs are butterflies. Conclusion II fails too.

Since we found one legitimate arrangement, consistent with both given statements, where both conclusions are false, neither conclusion can be said to always follow. The correct answer is (D), neither I nor II follows. $\boxed{\text{Neither conclusion follows}}$