Question

If $A,B$ and $C$ are non-empty sets then the 'Intersection of sets is distributive over union of sets' is represented as

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

Answer 1

Answer: (A)

$A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$

Let $A,B,C$ be any sets.

If we take intersection of sets, it should be distributive over union of sets.

Let's take union of $B$ and $C$ i.e. $B\cup C$ and then intersect with $A$.

$\therefore$ Finally we get $A\cap (B\cup C)$, which is same as union of intersection of $A,B$ and $A,C$.

i.e. $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$

Hence, option A is correct.