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.)