Question

Find, if the following sets are empty:

B = {x : x² + 4 = 0, x ∈ N}

Answer 1

B = {x : x² + 4 = 0, x ∈ N}

x² + 4 = 0

⇒ x² = -4

⇒ x = `sqrt(-4)` which is not a natural number.

But x ∈ N

∴ B = { }

∴ Given set B is an empty set.