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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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