Question

If $A,B$ and $C$ are any three sets, then $A\cap \left(B△C\right)=(A\cap B)\Delta (A\cap C)$ .If true enter 1 else 0.

Answer 1

$A\cap \left(B\Delta C\right)=A\cap \left[\right(B\cup C)-(B\cap C\left)\right]$

$\Rightarrow A\cap (B\cup C)-A\cap (B\cap C)$

$\Rightarrow (A\cap B)\cup (A\cap C)-(A\cap B)\cap (A\cap C)$

(using distributive low)

$\Rightarrow (A\cap B)\Delta (A\cap C)$