The question asks to count subsets, ordered pairs of subsets, or relations satisfying set-theoretic conditions such as disjointness, union, intersection, or element-overlap requirements.
Let A and B be non-empty sets consisting of digits. If $$A \cap B = A \cap \{ 0,2,4,6,8 \}$$ equality is satisfied, then A is called the common-intersection set of B. Given that set A is the common-intersection set of $$B = \{ 0,1,2,3,4 \}$$ how many different sets A are there? A) 3 B) 7 C) 15 D) 31 E) 63