List all the elements of each of the sets given below.
H = {x : x ϵ Z, |x| ≤ 2}.
Given x ∈ Z and |x| ≤ 2
Z is a set of integers
Integers are …-3, -2 , -1, 0, 1, 2, 3, …
Now, if we take x = -3 then we have to check that it satisfies the given condition |x| ≤ 2
|-3| = 3 > 2
So, -3 ∉ H
If x = -2 then |-2| = 2 [satisfying |x| ≤ 2]
So, -2 ∈ H
If x = -1 then |-1| = 1 [satisfying |x| ≤ 2]
∴ -1 ∈ H
If x = 0 then |0| = 0 [satisfying |x| ≤ 2]
∴ 0 ∈ H
If x = 1 then |1| = 1 [satisfying |x| ≤ 2]
⇒ 1 ∈ H
If x = 2 then |2| = 2 [satisfying |x| ≤ 2]
So, 2 ∈ H
If x = 3 then |3| = 3 > 2 [satisfying |x| ≤ 2]
So, 3 ∉ H
So, H = {-2, -1, 0, 1, 2}
So, E = {0, 1}