Prove that if A and B are sets such that A Union B notequalt

Prove that if A and B are sets such that A Union B notequalto emptyset, then A notequalto emptyset or B notequalto emptyset.

Solution

Answer :

Let A and B be any two sets such that A U B then there exists atleast one element x A U B.

Since A U B is the set of all elements of either the set A or the set B.

So that x A U B implies that x is in either the set A or x is in either the set B which means that either A or B .

hence, if A U B then either A or B .