Question

Which of the following is the empty set

• A. $\{ x : x$ is a real number and $\left. x ^ { 2 } - 1 = 0 \right\}$
• B. {x :x is a real number and $\left. x ^ { 2 } + 1 = 0 \right\}$
• C. {x :x is a real number and $\left. x ^ { 2 } - 9 = 0 \right\}$
• D. {x :x is a real number and $\left. x ^ { 2 } = x + 2 \right\}$

Answer 1

Answer: (B)

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

Answer 2

Since $x ^ { 2 } + 1 = 0$ gives $x ^ { 2 } = - 1$ $x = \pm i$

$\therefore$ x is not real but x is real (given)

$\therefore$ No value of x is possible.