Question

Let $A=\left\{x:x\in N\right\},B=\left\{x:x-2n,n\in N\right\},C=\left\{x:x=2n-1,n\in N\right\}$ and D = {x : x is a prime natural number}. Find:
(i) $A\cap B$
(ii) $A\cap C$
(iii) $A\cap D$
(iv) $B\cap C$
(v) $B\cap D$
(vi) $C\cap D$

Answer 1

$$\begin{gathered} A=\left\{x:x\in N\right\}=\{1,2,3,...\} \\ B=\left\{x:x-2n,n\in N\right\}=\{2,4,6,8,...\} \\ C=\left\{x:x=2n-1,n\in N\right\}=\{1,3,5,7,...\} \end{gathered}$$
D = {x:x is a prime natural number.} = {2, 3, 5, 7,...}
(i) $A\cap B$ = B
(ii) $A\cap C$ = C
(iii) $A\cap D$ = D
(iv) $B\cap C$ = $\mathrm{\varphi }$
(v) $B\cap D$ = {2}
(vi) $C\cap D$ = D$-${2}