Question

For any three sets A, B and C, $A\cap (B\cup C)$ is

• A. $(A\cup B)\cup (B\cap C)$
• B. $(A\cap B)\cup (A\cap C)$
• C. $A\cup (B\cap C)$
• D. $(A\cup B)\cap (B\cup C)$

Answer 1

The correct option is B $(A\cap B)\cup (A\cap C)$

In the problem statement we are taking union of $B$ and $C$ and then taking its intersection with $A$.

This means $A\cap (B\cup C)$will contain elements that are in $A$ and are in either $B$ or $C$.

$\therefore A\cap (B\cup C)$ is equivalent to taking intersection of $A,B$ and $A,C$ and then taking there union i.e. $(A\cap B)\cup (A\cap C)$

Hence, option B is correct.