Question

Which of the following are empty sets? Why? 

i. A = {a | a is a natural number smaller than zero} 

ii. B = {x | x² = 0} 

iii. C = {x | 5x – 2 = 0, x ∈ N}

Answer 1

i. A = {a| a is a natural number smaller than zero} 

Natural numbers begin from 1. 

∴ A = { } 

∴ A is an empty set. 

ii. B = {x | x² = 0} 

Here, x² = 0 

∴ x = 0 … [Taking square root on both sides] 

∴ B = {0} 

∴ B is not an empty set.

iii. C = {x | 5x – 2 = 0, x ∈ N} 

Here, 5x – 2 = 0 

∴ 5x = 2 

∴ x = 2/5 

Given, x ∈ N 

But, x = (2/5) is not a natural number. 

∴ C = { } 

∴ C is an empty set.