## Problem 1159

For P = {3,5,9,14}, Q = {1,6,12}, and R = {4,6,9,12}, find P U (Q∩R).

**Solution:-**

The union of sets A and B, denoted by A U B, is the set formed by combining all elements of A and all elements of B into one set. Symbolically, this is expressed by the equality

A U B = {x | x ϵ A or x ϵ B}.

Remember that the word ‘or’ is used to mean that x may be an element of set A or set B or both.

The intersection of sets A and B, denoted by A ∩ B, is the set of elements in set A that are also in set B. Symbolically, this is expressed by the equality A ∩ B = {x | x ϵ A and xϵ B}.

Determine the intersection of sets Q and R.

Q ∩ R = {6,12}

Determine the union of P and the intersection of Q and R.

(P U (Q ∩ R)) = {3,5,6,9,12,14}.