Question

For given sets A, B and C find the value of $A\cap (B-C)=(A\cap B)+(A\cap C)$

• A. True
• B. False

Answer 1

The correct option is B False

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

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

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

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

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

Hence False.