Question

Which of the following is a singleton set ?

• A. $\{x:x^2=5,x\epsilon N\}$
• B. $\{x:|x|=2,x\epsilon N\}$
• C. $\{x:|x|=7,x\epsilon Z\}$
• D. $\{x:x^2+4x+4=0,x\epsilon N\}$

Answer 1

The correct option is B $\{x:|x|=2,x\epsilon N\}$

a singleton set has only one element.

Option A

$⟶x^2=5⟹x=\pm \sqrt{5}$

which is an irrational number.

But $x\in N.$

So this a null set.

Option B

$⟶\left|x\right|=2.x=\pm 2\because x\in N$

represents natural numbers

So $x$ will assume only one value which is $2$.

i.e this is a singleton set.

Option C

$⟶\left|x\right|=7.x=\pm 7\because x\in Z$

represents integer

$x$ can assume two values $7,-7$.

i.e This is not a singleton set.

Option D

$⟶x^2+4x+4=0⟹{(x+2)}^2=0⟹x=-2.\because x\in N$

So this is a null set.

Ans- Option B.