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Question

Which of the following is a singleton set ?

A
{x:x2=5,xεN}
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B
{x:|x|=2,xεN}
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C
{x:|x|=7,xεZ}
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D
{x:x2+4x+4=0,xεN}
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Solution

The correct option is B {x:|x|=2,xεN}
a singleton set has only one element.

Option A
x2=5x=±5

which is an irrational number.
But xN.
So this a null set.

Option B
|x|=2.x=±2xN
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=±7xZ
represents integer

x can assume two values 7,7.
i.e This is not a singleton set.

Option D
x2+4x+4=0(x+2)2=0x=2.xN
So this is a null set.

Ans- Option B.

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