Question

List the elements of $A\cap B$, if $A=\{$ Even numbers $\},B=\{$ Even prime numbers $\}$.

Answer 1

Find the intersection of given sets:

Given, the two set $A=\{$ Even numbers $\},B=\{$ Even prime numbers $\}$

We know that, intersection of sets is the set of elements which are common in all the given sets.

Now, the set of even numbers $=\{2,4,6,......\}$ and set of prime numbers $=\{2,3,5,......\}$, this means $2$ is the only number which is even and prime both.

$\therefore$In the given two sets $A$ and $B$ the common element is $\left\{2\right\}$.

Hence, $A\cap B=$$\left\{2\right\}$.