Q1 of 145 Page 9

Which of the following are examples of the null set?

F = {x : x ϵ Q, 1 < x < 2}.


Here, x ∈ Q


i.e. x is a rational number


We know that,


If a and b are two rational numbers, then is a rational number between a and b such that


So, the rational number 1 and 2 is



∴ the set is not empty


∴ It is not a null set.


More from this chapter

All 145 →
1

Which of the following are examples of the null set?

D = {x : x ϵ N, x2 + 1 = 0}.


 1

Which of the following are examples of the null set?

E = {x : x ϵ W, x + 3 ≤ 3}.


 1

Which of the following are examples of the null set?

G = {0}


 2

Which of the following are examples of the singleton set?

(i) {x : x ϵ Z, x2 = 4}.


(ii) {x : x ϵ Z, x + 5 = 0}.


(iii) {x : x ϵ Z, |x| = 1}.


(iv) {x : x ϵ N, x2 = 16}.


(v) {x : x is an even prime number}