Final answer:
The shaded area in the Venn diagram of (A U (B ∩ C)) represents the union of set A with the intersection of sets B and C. It includes all elements in A, plus all elements that are in both B and C, thus the correct option is B. The intersection of sets A, B, and C.
Step-by-step explanation:
The shaded area in the Venn diagram of (A U (B ∩ C)) represents the union of set A with the intersection of sets B and C. This can be described as all elements that are in A, plus all elements that are in both B and C. If you imagine a Venn diagram, the shaded area would include the whole circle or region representing A (since it specifies the union with A), as well as the overlapping part between B and C (since it specifies the intersection of B and C).
Answer options:
- A. The union of sets A, B, and C would include all elements in any of the sets.
- B. The intersection of sets A, B, and C would include only the elements common to all three sets, which is not what (A U (B ∩ C)) represents.
- C. The complement of sets A, B, and C would include all elements not in those sets.
- D. The symmetric difference of sets A, B, and C would include elements that are in either of the sets, but not in their intersection.
Therefore, correct option is B. The intersection of sets A, B, and C.