Let R be the relation on Z defined by R = {(a | vedclass

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(A) The relation $R$ is defined on the set of integers $Z$ as $R = \{(a, b) : a, b \in Z, a - b \in Z\}$.Since the difference between any two integers

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Domain = $Z$,Range = $Z$

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(A) The relation $R$ is defined on the set of integers $Z$ as $R = \{(a, b) : a, b \in Z, a - b \in Z\}$.Since the difference between any two integers $a$ and $b$ is always an integer,every pair $(a, b)$ where $a, b \in Z$ satisfies the condition $a - b \in Z$.Therefore,$R = Z 	imes Z$.The domain of $R$ is the set of all first elements of the ordered pairs in $R$,which is $Z$.The range of $R$ is the set of all second elements of the ordered pairs in $R$,which is $Z$.Thus,the domain is $Z$ and the range is $Z$.

$A$. $f(x)=\frac{\|x+2\|}{x+2}, x \neq-2$	$1$. $[\frac{1}{3}, 1]$
$B$. $g(x)=\|[x]\|, x \in R$	$2$. $Z$
$C$. $h(x)=\|x-[x]\|, x \in R$	$3$. $W$
$D$. $f(x)=\frac{1}{2-\sin 3x}, x \in R$	$4$. $[0, 1)$
	$5$. $\{-1, 1\}$

Let $R$ be the relation on $Z$ defined by $R = \{(a, b) : a, b \in Z, a - b \text{ is an integer}\}$. Find the domain and range of $R$.

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