Final answer:
The set C united with the intersection of C and B (C ∪ (C ∩ B)) is equivalent to set C itself, making option b. C the correct answer.
Step-by-step explanation:
The question you've asked is about sets and set operations, specifically the union and intersection of sets. The union of sets, denoted as A OR B, is a set that contains all the elements that are in A, in B, or in both. The intersection of sets, denoted as A AND B, contains all elements that are both in A and in B.
In the expression C ∪ (C ∩ B), it refers to the set C united with the intersection of sets C and B. Now, any set intersected with itself is the set itself, which means C ∩ B is the set of all elements that are both in C and B. When you unite set C with any subset of itself, the result is still set C since C already includes all its elements.
Therefore, the set that is equivalent to C ∪ (C ∩ B) is simply set C, which corresponds to option b. C.