Question

3. Which of the following sets 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, xeN}​

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 setRead more on Sarthaks.com - https://www.sarthaks.com/845936/which-of-the-following-are-empty-sets-why-i-a-a-a-is-a-natural-number-smaller-than-zero-ii-b-x-x-2?show=845941#a845941