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

1.	List all the elements of each of the sets given below. H = {x : x ϵ Z, \|x\| ≤ 2}.
Answer» 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}

List all the elements of each of the sets given below. H = {x : x ϵ Z, |x| ≤ 2}.

Answer»

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}