Answer each of the following and justify your answer. Complete parts (a) through (b) below.
a. If a∈A ∪ B, is it true that a∈A ∩ B? Choose the correct answer below.
A.
Yes, because an intersection of two sets always contains more elements than the union of the two sets.
B.
Yes, because if an element is in the union of two sets, it is always in the intersection of the two sets.
C.
No, because (A ∪ B) ∩ (A ∩ B) is ∅.
D.
No, because if an element is in the union of two sets, it is not necessarily in the intersection of the two sets.