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}

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 =± i
∴ x is not real but x is real (given)
∴ No value of x is possible.

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