Which of the following is an empty set Options: A . &nbsp{x:x is a real number and x2−1=0} B . &nbsp{x:x is a real number and x2+1=0} C . &nbsp{x:x is a real number and x2−9=0} D . &nbsp{x:x is a real number and x2=x+2}

Answer: Option B : B Since x 2 + 1 = 0, gives x 2 = − 1 ⇒ x = ± i ∴ x is not real but x has to be is real (given) ∴ No real value of x is possible in this case.

Which of the following is an empty set

Question

Which of the following is an empty set

Options:

A . {x:x is a real number and x2−1=0}

B . {x:x is a real number and x2+1=0}

C . {x:x is a real number and x2−9=0}

D . {x:x is a real number and x2=x+2}

Answer: Option B
:
B
Since

x^{2}

+ 1 = 0, gives

x^{2} = - 1

⇒

x = \pm i

∴

x

is not real but

x

has to be is real (given)
∴ No real value of

x

is possible in this case.

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