Question

Comment true or false on the following statements
$A\cap (B-C)=(A\cap B)-(A\cap C)$

• A. True
• B. False

Answer 1

The correct option is A True

Let $x\in A\cap (B-C)$

$\Rightarrow x\in A$ and $x\in (B-C)$

$\Rightarrow x\in A$ and $(x\in B\text{and}x\notin C)$

$\Rightarrow (x\in A\text{and}x\in B)$ and $(x\in A\text{and}x\notin C)$

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

Hence true.