Question

Statement I The set $\{x: x$ is a real number and $\left.x^2-1=0\right\}$ is the empty set.
Statement II The set $A=\left\{x: x \in R, x^2=16\right.$ and $2 x=6\}$ 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 $2 x=6$
$x=4,-4 \text { and } x=3$
$\therefore$ There is no real $x$ which simultaneously satisfied $x^2=16$ and $2 x=6$
So, Statement II is true.