Q.If A = (-7, 3], B = [2, 6] and C = [4, 9] then find A∩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 …