Circle D is inside of circle A. Circle A overlaps with circle B. Circle B also overlaps with circle C.

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.

Answer 1

Based on the description of the circles and their relationships, let's analyze each statement:

1. Only sets A, B, and C are subsets of the universal set, U.

   • This statement is incorrect because set D, which is inside circle A, is also a subset of the universal set, U. Thus, sets A, B, C, and D are all subsets of U.

2. The intersection of sets A and C is set B.

   • This statement is also incorrect. The intersection of sets A and C would refer to the elements that are common to both A and C. Since we know that A overlaps with B and B overlaps with C, but there is no information suggesting the overlap between A and C corresponds to set B specifically.

3. Set D is a subset of set A.

   • This statement is correct because circle D is entirely contained within circle A, indicating that all elements of D are also part of A.

4. The union of sets B and C is the overlapping shaded region in the middle of the two sets.

   • This statement is incorrect. The union of sets B and C includes all elements that are in B, in C, or in both, which is larger than just the overlapping region. The overlapping region refers to the intersection of B and C, not the union.

Thus, the correct statement is: Set D is a subset of set A.