Question

State infinite/ singleton/ null set/ not a set : { x : 15 ≤x<15 and x=W}​

Answer 1

a singleton set has only one element.

Option A

⟶x

2

=5

⟹x=±

5

which is an irrational number.

But x∈N.

So this a null set.

Option B

⟶∣x∣=2.

x=±2

∵x∈N

represents natural numbers

So x will assume only one value which is 2.

i.e this is a singleton set.

Option C

⟶∣x∣=7.

x=±7

∵x∈Z

represents integer

x can assume two values 7,−7.

i.e This is not a singleton set.

Option D

⟶x

2

+4x+4=0

⟹(x+2)

2

=0

⟹x=−2.

∵x∈N

So this is a null set.

Answer 2

(2x + 1)/3 + 15 < 17; x ∈ W

⇒ (2x + 1)/3 ≤ 17 – 15 = 2

2x + 1 ≤ 6 ⇒ 2x ≤ 5

⇒ x ≤ (5/2) = 2. ½

But x ∈ W

∴ x = 0, 1, 2

∴ Solution set is = {0, 1, 2}