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Which of the following is the empty set?...

Which of the following is the empty set?

A

{x : x is a real number and `x^(2) - 1 = 0`}

B

{x : x is a real number and `x^(2) + 1 = 0`}

C

{x : x is a real number and `x^(2) - 9 = 0`}

D

{x : x is a real number and `x^(2) = x + 2`}

Text Solution

Verified by Experts

The correct Answer is:
B
`x^(2) - 1 = 0`
`implies x = - 1, 1`
`therefore` x is real, q `x^(2) + 1 = 0`
`implies x = pm i`
`therefore` x is not real, `x^(2) - 9 = 0`
`x = pm 3`
`therefore` x is real `x^(2) - x - 2 = 0`
implies x = 2, -1
`therefore` x is real.
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