1.

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»

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, x = 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 = is not a natural number. 

∴ C = { } 

∴ C is an empty set.



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