Final answer:
Based on the provided information, set A and set B overlap with the number 14, but since set A and set C do not share any elements (P(A AND C) = 0), there are no numbers in set A that are elements of both set B and set C. The given options for the answer do not match this conclusion, suggesting that further clarification is needed for the question.
Step-by-step explanation:
Given the question "Which numbers in set A = {-7, -4, -2, 14, 21, 34, 42} are elements of both set B and set C?", and based on the provided information that set A AND B contains {14, 16, 18}, we can immediately identify that the numbers 14, 16, and 18 are the only elements in set A that could also be in set B, since they are mentioned in the intersection of sets A and B. However, since 16 and 18 are not elements of set A, we are only left with 14 as the element of set A that is definitely in set B.
Next, for set C, no specific elements are given, but the information states that sets A and C do not have any numbers in common and so P(A AND C) = 0, meaning they are mutually exclusive. Therefore, there are no elements in set A that are also in set C. With this in mind, the answer to which numbers in set A are elements of both set B and set C is none, since set A and set C are mutually exclusive. However, it's important to note that the available options provided do not reflect the correct answer based on the information given, and it might be necessary to review the question or seek clarification.