- Home
- Standard 12
- Mathematics
1.Relation and Function
hard
A relation on the set $A\, = \,\{ x\,:\,\left| x \right|\, < \,3,\,x\, \in Z\} ,$ where $Z$ is the set of integers is defined by $R= \{(x, y) : y = \left| x \right|, x \ne - 1\}$. Then the number of elements in the power set of $R$ is
A
$32$
B
$16$
C
$8$
D
$64$
(JEE MAIN-2014)
Solution
$A = \left\{ {x:\left| x \right| < 3,x \in Z} \right\}$
$A = \left\{ { – 2, – 1,0,1,2} \right\}$
$R = \left\{ {\left( {x,y} \right):y = \left| x \right|,x \ne – 1} \right\}$
$R = \left\{ {\left( { – 2,2} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,2} \right)} \right\}$
$R$ has four elements
Number of elements in the power set of $R$
$ = {2^4} = 16$
Standard 12
Mathematics
