Question

B = {x : x + 5 = 5} is not an empty set. Why? 

Answer 1

B = {x: x + 5 = 5} is not an empty set 

let x ∈ Z or x ∈ W 

then for x = 0 ⇒ x + 5 = 0 + 5 = 5 

So if x ∈ W, or x ∈ Z then for x = 0, 

x + 5 = 5 is true. 

Then the set B = {0} which is not an empty set. 

Note: But if x ∈ N 

We will have no ‘x’ such that x + 5 = 5 

then ‘B’ will be an empty set. 

But in the textbook it is not given whether x ∈ N (or) x ∈ W (or) x ∈ Z. 

Hence we consider first one.