Q.If aN = {ax : x ∈N}, then set 6N∩8N = A) 8N B) 48N C) 12N D) 24N

The intersection of two sets A and B, written A ∩ B, collects only the elements that are in BOTH A and B simultaneously: A ∩ B = {x / x∈A and x∈B}. Visually, this is just the overlapping (lens-shaped) region shared by the two sets on a Venn diagram. If two sets share no elements at all, A ∩ B = φ, and the sets are called DISJOINT. Like union, intersection is commutative (A∩B = B∩A) and associative ((A∩B)∩C = A∩(B∩C)). Intersecting with the empty set always gives the empty set (φ∩A = φ), and intersection is idempotent (A∩A = A). Both A∩B ⊆ A and A∩B ⊆ B always hold — intersection can only shrink a set, never grow it. Intersection distributes over union (and vice versa): A∩(B∪C) = (A∩B)∪(A∩C), and A∪(B∩C) = (A∪B)∩(A∪C) — these are the two distributive laws of set algebra, directly analogous to how multiplication distributes over addition in ordinary arithmetic. De Morgan's second law connects intersection with complement: (A∩B)' = A'∪B'.