Question

Which of the following are examples of the null set:
$\left(i\right)$ Set of odd natural numbers divisible by $2$
$\left(ii\right)$ Set of even prime numbers
$\left(iii\right)$ $\{x:x$ is a natural number, $x<5$ and $x>7\}$
$\left(iv\right)$ $\{y:y$ is a point common to any two parallel lines$\}$

Answer 1

$\left(i\right)$ Since odd numbers are not divisible by 2, So given set is a null set

$\left(ii\right)$ Set of even prime numbers are not a null set as $2$ is an even prime number. So, given set is not a null set.

$\left(iii\right)$ A number cannot be both less than $5$ and greater than $7.$ So, given set is a null set.

$\left(iv\right)$ The parallel lines do not intersect, therefore they do not have any common points. So, given set is a null set.