Question

Which of the following are examples of the null set?

i) Set of odd natural numbers divisible by $2$.

ii) set of even prime numbers.

iii) $\{x:x\text{is a natural number},x<5andx>7\}$

iv) $\{y:y\text{is a point common to any two parllel lines}\}$

Answer 1

i) Since odd numbers are not divisible by $2$

so given set is a null set.

ii) set of even prime numbers is not a null set as $2$ is an even prime number.

So, given set is not a null set.

iii) A number cannot be both less than $5$ and greater than $7$.

So, given set is a null set.

iv) $\because$ The parllel lines do not intersect.

$\therefore$ They have no common point.

So, given set is a null set.