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

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

Answer»

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.

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