Question

Statement I The set $\{x:x$ is a real number and $x^2-1=0\}$ is the empty set.
Statement II The set $A=\{x:x\in R,x^2=16$ and $2x=6\}$ is an empty set.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (B)

The set of real numbers which satisfy $x^2-1=0$, is $\{-1,1\}$.
So, Statement $I$ is false.
Given, $x^2=16$ and $2x=6$
$x=4,-4\text{ and }x=3$
$\therefore$ There is no real $x$ which simultaneously satisfied $x^2=16$ and $2x=6$
So, Statement II is true.