Introduction to Set Operations

Problem

If A and B are sets, then their union A∪B is the set comprising any elements in either A or B; their intersection A∩B is the set of elements in both A and B; and their set difference A−B is the set of elements in A but not in B.

Furthermore, if A is a subset of another set U, then the set complement of A with respect to U is defined as the set Ac=U−A. See the Sample sections below for examples.

Given: A positive integer n (n≤20,000) and two subsets A and B of {1,2,…,n}.

Return: Six sets: A∪B, A∩B, A−B, B−A, Ac, and Bc (where set complements are taken with respect to {1,2,…,n}).