Question

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.

Explanation:

1. Analyze the first option: All elements in A, B, C, D are within U, so all (A, B, C, D) are subsets of U. So this option is wrong.
2. Analyze the second option: Intersection of A and C—looking at the Venn diagram, A and C do not overlap directly; B overlaps with both A and C. So the intersection of A and C is not B. This option is wrong.
3. Analyze the third option: Set D is entirely inside set A (as D is a circle within A's circle). By definition of a subset (all elements of D are in A), D is a subset of A. This seems correct.
4. Analyze the fourth option: Union of B and C is all elements in B or C (including their overlapping and non - overlapping regions). The overlapping shaded region in the middle of B and C is their intersection, not their union. So this option is wrong.

Answer:

C. Set D is a subset of set A.