Question

Which of the following is an 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}

Answer 1

The correct option is B

{x:x is a real number and $x^2$ +1 = 0}

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.