Question

Let $U=\{1,2,\mathrm{3...}20\}$, Let $A,B$ and $C$ be the subsets of $U$. Let $A$ be the set of all numbers, which are perfect square, $B$ be the set of all numbers which are multiples of $5$ and $C$ be the set of all numbers, which are divisible by $2$ and $3$?
Consider the following statements.Prove that $A,B$ and $C$ mutually exclusive.

Answer 1

Given, $U=\{1,2,\mathrm{3...}20\}$, Let $A,B$.

According to the problem,

$A=\{1,4,9,16\}$,

$B=\{5,10,15\}$,

$C=\{6,12,18\}$.

Now it is clear that $A\cap B\cap C=\varphi$.

So $A,B,C$ are mutually exclusive.