13. Five mark exercise problems V

If \(A = \{x: x = 6n, n \in W \ \text{and} \ n < 6\}\), \(B = \{x: x = 2n, n \in N \ \text{and} \ 2 < n \leq 9\}\) and \(C = \{x: x = 3n, n \in N \ \text{and} \ 4 \leq n < 10\}\), show that \(A - (B \cap C) = (A - B) \cup (A - C)\).

 

Proof:

 

\(B \cap C =\) $\left\{i,i\right\}$

 

\(A - (B \cap C) =\) $\left\{i,i,i,i\right\}$ ---- (\(1\))

 

\(A - B =\) $\left\{i,i,i\right\}$

 

\(A - C =\) $\left\{i,i,i\right\}$

 

\((A - B) \cup (A - C) =\) $\left\{i,i,i,i\right\}$ ---- (\(2\))

 

From equations (\(1\)) and (\(2\)), \(A - (B \cap C) = (A - B) \cup (A - C)\).

 

Hence, we proved.

 

(Note: Enter the numbers in ascending order.)