Question

Eight sets A, B, C, D, E, F, G and H are such that:

A is a superset of B, but subset of C.
B is a subset of D, but superset of E.
F is a subset of A, but superset of B.
G is a superset of D, but subset of F.
H is a subset of B.

N(A), N(B), N(C), N(D), N(E), N(F), N(G) and N(H) are the number of elements in the sets A, B, C, D, E, F, G and H respectively.

Which one of the following could be FALSE, but not necessarily FALSE?

• A. E is a subset of D
• B. E is a subset of C
• C. E is a subset of A
• D. E is a subset of H

Hint:

Build the chain of set sizes from the passage; E and H are never directly compared, so any statement linking them is left undecided.

Answer 1

The Correct Option is D

This question is about which containment relationships are locked in by the passage and which are left open. The safest way to check is to picture the sets as one nested arrangement and see what is actually forced.

Reading the eight lines of the passage as a picture: H sits inside B, and E also sits inside B, but nothing tells us how H and E sit relative to each other. From B outward, the picture widens step by step: B sits inside D, D sits inside G, G sits inside F, F sits inside A, and A sits inside C. So starting from E and moving outward, we pass through B, D, G, F, A, and finally C, in that fixed order.

1. E is a subset of D: forced true, because E sits inside B and B sits inside D, so E is automatically inside D too.
2. E is a subset of C: forced true, because the whole outward chain from E eventually lands inside C.
3. E is a subset of A: forced true, for the same reason, since A appears on that same outward chain before C.
4. E is a subset of H: this pairs up two sets, E and H, that both sit inside B but were never compared with each other anywhere in the passage. Nothing forces E inside H, and nothing forbids it either.

So the first three statements are always true and can never be false, while the fourth one is genuinely open: it might hold in one valid arrangement of the sets and fail in another.

Let's summarize:

• Every relationship that follows the passage's outward chain, from E to B to D to G to F to A to C, is always true.
• E and H were never compared to each other, so any statement linking them directly is undecided, not fixed.

Since "E is a subset of H" is the only statement not pinned down by the passage, it is the one that could be false without being necessarily false. The answer is option (D).