Q. 4 H5.0( 4 Votes )

# 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}

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