Question

Given A $=\{1,2,3,4\}$, B $=\{3,4,5,6\}$ and C $=\{6,7\}$. Verify that (A $\cap$ B) $\cap$ C = A $\cap$ (B $\cap$ C).

Answer 1

Given that:

$A=\{1,2,3,4\},B=\{3,4,5,6\}$ and $C=\{6,7\}$

$A\cap B=\{3,4\}$

$L.H.S.=(A\cap B)\cap C=\left\{\varphi \right\}$

Now,

$B\cap C=\left\{6\right\}$ and

$R.H.S.=A\cap (B\cap C)=\left\{\varphi \right\}$

$\therefore L.H.S=R.H.S$