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

The union of two sets A and B, written A ∪ B, collects every element that is in A OR in B (using 'or' inclusively — an element in both still counts, just once): A ∪ B = {x / x∈A or x∈B}. Visually, on a Venn diagram, A ∪ B is the entire region covered by A together with B, overlap included. Union obeys several algebraic laws that make it behave much like ordinary addition in some ways: it is commutative (A∪B = B∪A) and associative ((A∪B)∪C = A∪(B∪C)), so the order and grouping of a union chain never matters. The empty set is its identity element (A∪φ = A, changing nothing), and it is idempotent (A∪A = A, unioning a set with itself changes nothing). A useful co …