Question

8.
Which one of the following is a singleton set?
(i) {X/X = X XER}
(ii) {X/X2 = -1, XER}
(iii) x/2x = 0)
(iv) {X/3x + 2 = 0XEN)
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)​

Answer 1

Answer:

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.