Question

The set $A=\mathrm{\{}x:x$ belongs to $\mathrm{ℝ},x^2=16$ and $2x=6\}$ is equal to

• A. $\varnothing$
• B. $\left\{14,3,4\right\}$
• C. $\left\{3\right\}$
• D. $\left\{4\right\}$

Answer 1

The correct option is A

$\varnothing$

Explanation for the correct option

Given: $A=\mathrm{\{}x:x$ belongs to $\mathrm{ℝ},x^2=16$ and $2x=6\}$

$$\begin{gathered} x^2=16 \\ \Rightarrow x=\pm 4 \end{gathered}$$

$$\begin{gathered} 2x=6 \\ \Rightarrow x=3 \end{gathered}$$

$\therefore$No value of $x$ satisfies the given conditions.

Therefore, $A=\varnothing$ (empty set )

Hence the correct option is option A.