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 A∪B.

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 …