A relation on the set A = {x : |x|

Question

(B) Given the set $A = \{x : |x| < 3, x \in Z\}$.Since $|x| < 3$ and $x$ is an integer,the elements of $A$ are $\{-2, -1, 0, 1, 2\}$.The relation $R$

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(B) Given the set $A = \{x : |x| Since $|x| The relation $R$ is defined as $R = \{(x, y) : y = |x|, x 
eq -1\}$.For each $x \in A$ such that $x 
eq -1$,we find the corresponding $y = |x|$:If $x = -2$,$y = |-2| = 2$. So,$(-2, 2) \in R$.If $x = 0$,$y = |0| = 0$. So,$(0, 0) \in R$.If $x = 1$,$y = |1| = 1$. So,$(1, 1) \in R$.If $x = 2$,$y = |2| = 2$. So,$(2, 2) \in R$.Thus,$R = \{(-2, 2), (0, 0), (1, 1), (2, 2)\}$.The number of elements in $R$ is $n(R) = 4$.The number of elements in the power set of $R$ is given by $2^{n(R)} = 2^4 = 16$.

$A$ relation on the set $A = \{x : |x| < 3, x \in Z\}$,where $Z$ is the set of integers,is defined by $R = \{(x, y) : y = |x|, x \neq -1\}$. Then the number of elements in the power set of $R$ is

Similar Questions

$R$ is a relation on $\mathbb{N}$ given by $R=\{(x, y): 4x+3y=20\}$. Which of the following belongs to $R$?

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a+2 b=27$. Then $R$ is:

Let $A = \{1, 2, 3, \ldots, 14\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : 3x - y = 0, \text{ where } x, y \in A\}$. Write down its domain,codomain,and range.

In the context of a power set containing a subset,the relation 'is a subset of' $(\subseteq)$ is:

If $n(A)=2$ and the total number of possible relations from set $A$ to set $B$ is $1024$,then $n(B)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module