Question

The relation on the set $A=\{x:1<|x|\le 4,x\in Z\}$ is defined by $R=\left\{\right(x,y):y=|x|\}.$ Then the number of elements in the power set of $R$ is

• A. $16$
• B. $32$
• C. $64$
• D. $128$

Answer 1

The correct option is C $64$

$A=\{x:1<|x|\le 4,x\in Z\}$
$\Rightarrow |x|>1$ and $|x|\le 4$
$\Rightarrow x\notin \{-1,1\}$ and $x\in [-4,4]$
$\therefore x\in [-4,-1)\cup (1,4]\therefore A=\{-4,-3,-2,2,3,4\}$

Now, $R=\left\{\right(x,y):y=|x|\}\Rightarrow R=\left\{\right(-4,4),(-3,3),(-2,2),(2,2),(3,3),(4,4\left)\right\}$
$\therefore$ Number of elements in power set of $R$ is $2^6=64$