14. Five mark exercise problems VI

If $A = \{y: y = \frac{a + 1}{2}, a \in W \ \text{and} \ a \leq 5\}$, $B = \{y: y = \frac{2n - 1}{2}, n \in W \ \text{and} \ n < 5\}$ and $C =$ $\left\{-1,-\frac{1}{2},1,\frac{3}{2},2\right\}$, show that $A - (B \cup C) = (A - B) \cap (A - C)$.

 

Proof:

 

$B \cup C =$ $\left\{i,\frac{i}{i},\frac{i}{i},i,\frac{i}{i},i,\frac{i}{i},\frac{i}{i}\right\}$

 

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

 

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

 

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

 

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

 

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

 

Hence, we proved.

 

(Note: Enter the numbers in ascending order.)