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) $$\left \{ x : x \text { is a natural numbers, $$x < 5$$ and $$x > 7}\right \}$$
(iv) $$\left \{ y : y \text { is a point common to any two parallel lines}\right \}$$

Answer 1

(i) A set of odd natural numbers divisible by $2$ is a null set because no odd number is divisible by $2$.
(ii) $A=\left\{2\right\}$.
A set of even prime numbers is not a null set because $2$ is an even prime number.
(iii) $\{x:x\text{is a natural number},x<5\text{and}x>7\}$ is a null set because a number cannot be simultaneously less than $5$ and greater than $7$.
(iv) $\{y:y\text{is a point common to any two parallel lines}\}$ is a null set because parallel lines do not intersect. Hence, they have no common point.