List all the elements of each of the sets given below.E = {x : x ϵ Z

1.	List all the elements of each of the sets given below.E = {x : x ϵ Z and x2 = x}.
Answer» Given: x ∈ Z and x² = x Z is a set of integers Integers are …-2 , -1, 0, 1, 2, … Now, if we take x = -2 then we have to check that it satisfies the given condition x² = x(-2)² = 4 ≠ 2 So, -2 ∉ E If x = -1 then (-1)² = 1 ≠ -1 [not satisfying x² = x] So, -1 ∉ E If x = 0 then (0)² = 0 [satisfying x² = x] ∴ 0 ∈ E If x = 1 then (1)² = 1 [satisfying x² = x] ∴ 1 ∈ E If x = 2 then (2)² = 4 ≠ 2 [not satisfying x² = x] ⇒ 2 ∉ E So, E = {0, 1}

List all the elements of each of the sets given below.E = {x : x ϵ Z and x2 = x}.

Answer»

Given: x ∈ Z and x² = x

Z is a set of integers

Integers are …-2 , -1, 0, 1, 2, …

Now, if we take x = -2 then we have to check that it satisfies the given condition x² = x(-2)² = 4 ≠ 2

So, -2 ∉ E

If x = -1 then (-1)² = 1 ≠ -1 [not satisfying x² = x]

So, -1 ∉ E

If x = 0 then (0)² = 0 [satisfying x² = x]

∴ 0 ∈ E

If x = 1 then (1)² = 1 [satisfying x² = x]

∴ 1 ∈ E

If x = 2 then (2)² = 4 ≠ 2 [not satisfying x² = x]

⇒ 2 ∉ E

So, E = {0, 1}