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

Solution:

(i) A set of odd natural numbers divisible by 2 is a null set because there is no odd number that is divisible by 2.

(ii) A set of even prime numbers is not a null set because there exists a number, which is 2, that is an even prime number.

(iii) {x: x is a natural number, x < 5 and x > 7} is a null set because no number can be simultaneously less than 5 and greater than 7.

(iv) {y: y is a point common to any two parallel lines} is a null set because parallel lines do not intersect at any point and hence they have no common point.

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.2 Question 1

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}

Summary:

We are asked to find which of the given sets are examples of the null set. We found that
(i) Set of odd natural numbers divisible by 2 is a null set.
(ii) Set of even prime numbers is NOT a null set.
(iii) {x : x is a natural numbers, x < 5 and x > 7} is a null set.
(iv) {y : y is a point common to any two parallel lines} is a null set.