Q.If U = {x/x∈N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8 9, 12}. Write down the set B∩C.

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 …