Question

State whether the following statement is an empty set or not? why?

C = {x | 5x - 2 = 0, x ∈ N}

Answer 1

⇒ 5x - 2 = 0

⇒ 5x = 2

⇒ x = `2/5`          

We know that natural number, N = {1, 2, ...}

∴ C = {x | 5x - 2 = 0, x ∈ N} = {}

∴ C is an empty set.