7. Five mark example problems III

If \(P = \{x: x \in W \ \text{and} \ 0 < x < 10\}\), \(Q = \{x: x = 2n + 1, n \in W \ \text{and} \ n < 5\}\) and \(R = \{2, 3, 5, 7, 11, 13\}\), then verify \(P - (Q \cap R) = (P - Q) \cup (P - R)\).

 

Proof:

 

\(P =\)

 

\(Q =\)

 

\(R = \{2, 3, 5, 7, 11, 13\}\)

 

\(Q \cap R =\)

 

\(P - (Q \cap R) =\)  ---- (\(1\))

 

\(P - Q =\)

 

\(P - R =\)

 

\((P - Q) \cup (P - R) =\)  ---- (\(2\))

 

From equations (\(1\)) and (\(2\)), \(P - (Q \cap R) = (P - Q) \cup (P - R)\).

 

Hence, we proved.