Question

State whether given set is empty or not?
$\{x:x$ is a natural numbers, $x<5$ and $x>7\}$

Answer 1

Solution:- Empty

Empty set $\left(\varphi \right)$: which has no elements

Natural numbers $=1,2,3,4,...........$

Natural numbers less than 5, $(x<5)=1,2,3,4$

Natural numbers greater than 7, $(x>7)=8,9,10,.........$

$\because$ A number can not be simultaneously less than 5 and greater than 7.

Hence, the set of natural numbers less than 5 and greater than 7 is empty.