A relation on the set $\mathrm{A}=\{\mathrm{x}:|\mathrm{x}| < 3, \mathrm{x} \in \mathrm{Z}\}$, where $Z$ is…
A relation on the set $\mathrm{A}=\{\mathrm{x}:|\mathrm{x}| < 3, \mathrm{x} \in \mathrm{Z}\}$, where $Z$ is the set of integers is defined by $\mathrm{R}=\{(\mathrm{x}, \mathrm{y}): \mathrm{y}=|\mathrm{x}|, \mathrm{x} \neq-1\}$. Then the number of elements in the power set of $R$ is:
32
16
8
64
Solution
$
\begin{aligned}
&\mathrm{A}=\{x:|x| < 3, x \in Z\} \\
&\mathrm{A}=\{-2,-1,0,1,2\} \\
&\mathrm{R}=\{(x, y): y=|x|, x \neq-1\} \\
&\mathrm{R}=\{(-2,2),(0,0),(1,1),(2,2)\}
\end{aligned}
$
$\mathrm{R}$ has four elements
Number of elements in the power set of $\mathrm{R}$
$
=2^4=16
$