Which of the following is the empty set

Options

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`}

Answer

B

Explanation

`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.