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Circle D is inside of circle A. Circle A overlaps with circle B. Circle B also overlaps with circle C.
Based on the Venn diagram, which of the following statements is correct?
Only sets A, B, and C are subsets of the universal set, U.
The intersection of sets A and C is set B.
Set D is a subset of set A.
The union of sets B and C is the overlapping shaded region in the middle of the two sets.
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Correct statement: "Set D is a subset of set A."
Explanation: D lies entirely inside A, so every element of D is also an element of A (D ⊆ A).
Why the others are wrong:
- "Only A, B, and C are subsets of U" is false — all sets shown (including D) are subsets of the universal set U.
- "The intersection of A and C is B" is false — B is a separate set that overlaps A and C, but A ∩ C is not equal to B (it may be empty or a different region).
- "The union of B and C is the overlapping shaded region" is false — that shaded region is B ∩ C (the intersection); the union B ∪ C is all points in either B or C.
Explanation: D lies entirely inside A, so every element of D is also an element of A (D ⊆ A).
Why the others are wrong:
- "Only A, B, and C are subsets of U" is false — all sets shown (including D) are subsets of the universal set U.
- "The intersection of A and C is B" is false — B is a separate set that overlaps A and C, but A ∩ C is not equal to B (it may be empty or a different region).
- "The union of B and C is the overlapping shaded region" is false — that shaded region is B ∩ C (the intersection); the union B ∪ C is all points in either B or C.
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