In complement of a set if U be the universal set and A a subset of U,

then the complement of A is the set of all elements of U which are not the elements of A.

Symbolically, we denote the complement of A with respect to U as A bar or A dash.

For Example; If U = {1, 2, 3, 4, 5, 6, 7} and A = {1, 3, 7} find complement of A

Solution:

We observe that 2, 4, 5, 6 are the only elements of U which do not belong to A.

So, complemet of A = {2, 4, 5, 6}

Again

1. The complement of a universal set is an empty set.

2. The complement of an empty set is a universal set.

3. The set and its complement are disjoint sets.