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 is a natural number, x < 5 and x > 7}

(iv) { y : y is a point common to any two parallel lines}

Answer 1

(i) Set of odd natural numbers divisible by 2 is an empty set because odd natural numbers are not divisible by 2.

(ii) Set of even prime numbers is {2} which is not empty set.

(iii) {x : s is a natural number, x < 5 and x > 7} is an empty set because there is no natural number which satisfies simultaneously x < 5 and x > 7.

(iv) {y : y is a point common to any two parallel lines} is an empty set because two parallel lines do not have a common point.