Question

Give reasons for the following statements:-
$\left\{2,3,5,7,9,11\right\}\ne \{x:x$ is a prime number$x<12\}$

Answer 1

A number which has only two factors the number itself and $1$ is called a prime number.

$\{2,3,5,7,9,11\}$

Here $2,3,5,7,11$ are prime numbers $\because$ they have only two factors.

But the element $9$ has $3$ factors.

Consider the set $\{x:xisaprimenumberx<12\}$

$=\{2,3,5,7,11\}$

Thus,$\{2,3,5,7,9,11\}\ne \{2,3,5,7,11\}$

Hence $\{2,3,5,7,9,11\}\ne \{x:xisaprimenumberx<12\}$