The relation on the set A-x -1- x- 4- x - Z is defined by R-x-y-y-x- Then the number of elements in the power set of R is

A={x :1| x|≤ 4, x ∈ Z } ⇒ |x| 1 and |x| ≤ 4 ⇒ x∉{ 1,1} and nbsp; nbsp;x∈[ 4,4] ∴ x ∈ [ 4, 1) ∪ (1,4] ∴ A={ 4, 3, 2,2,3,4} nbsp; Now, R={(x,y):y=|x| } ⇒ ...

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Standard XI

Mathematics

Cardinality of Power Set of a Set

The relation ...

Question

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

16

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64

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Solution

The correct option is C $64$
$A = {x : 1 < | x | \leq 4, x \in Z}$
$\Rightarrow | x | > 1$ and $| x | \leq 4$
$\Rightarrow x \notin {- 1, 1}$ and $x \in [- 4, 4]$
$∴ x \in [- 4, - 1) \cup (1, 4] ∴ A = {- 4, - 3, - 2, 2, 3, 4}$

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

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Depict this relationship using roster form

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

The correct option is C 64A={x:1<|x|≤4,x∈Z } ⇒|x|>1 and |x|≤4 ⇒x∉{−1,1} and x∈[−4,4] ∴x∈[−4,−1)∪(1,4]∴A={−4,−3,−2,2,3,4} Now, R={(x,y):y=|x|}⇒R={(−4,4),(−3,3),(−2,2),(2,2),(3,3),(4,4)} ∴ Number of elements in power set of R is 26=64

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