Question

Let $$A=\{x : x\in N\}, B=\{x : x=2n, n\in N\}, C=\{x : x=2n-1, n\in N\}$$ and $$D=\{x : x$$ is a prime natural number$$\}$$. Find $$A\cap B$$.

Answer 1

The given sets are:

$$A=\left\{x:x\in N \right\}=\left\{1,2,3,4..... \right\}$$

$$B=\left\{x:x=2n, n\in N \right\}=\left\{2,4,6,8,10.... \right\}$$

$$C=\left\{x:x=2n-1, n\in N \right\}=\left\{1,3,5,7,9....... \right\}$$

$$D=\left\{x:x\ is\ a\ prime\ number \right\}=\left\{2,3,5,7,11,13.... \right\}$$

$$\therefore \ A\cap B=\left\{1,2,3,4.... \right\} \cap \left\{2,4,6,8.... \right\}$$

$$=\left\{2,4,6,8.... \right\}$$

$$=B$$

Hence $$\boxed {A\cap B=B}$$