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Let $S$ denote set of all integers. Define a relation $R^{\circ}$
$' a R b$ if $a b \geq 0$ where $a, b \in S^{\prime}$. Then $R$ is:
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$' a R b$ if $a b \geq 0$ where $a, b \in S^{\prime}$. Then $R$ is:
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Verified Answer
The correct answer is:
An equivalence relation
$\mathrm{S}=$ Set of all integers and $\mathrm{R}=\{(\mathrm{a}, \mathrm{b}), \mathrm{a}, \mathrm{b} \in \mathrm{S}$ and $\mathrm{ab} \geq 0\}$
For reflexive $: \mathrm{aRa} \Rightarrow \mathrm{a}, \mathrm{a}=\mathrm{a}^{2} \geq 0$
for all integers a. $\mathrm{a} \geq 0$ For symmetric $: \mathrm{aRb} \Rightarrow \mathrm{ab} \geq 0 \forall \mathrm{a}, \mathrm{b} \in \mathrm{S}$
If $a b \geq 0$, then $b a \geq 0 \Rightarrow b R a$
For transitive :
If $a b \geq 0, b c \geq 0$, then also ac $\geq 0$ Relation $\mathrm{R}$ is reflexive, symmetric and transitive
For reflexive $: \mathrm{aRa} \Rightarrow \mathrm{a}, \mathrm{a}=\mathrm{a}^{2} \geq 0$
for all integers a. $\mathrm{a} \geq 0$ For symmetric $: \mathrm{aRb} \Rightarrow \mathrm{ab} \geq 0 \forall \mathrm{a}, \mathrm{b} \in \mathrm{S}$
If $a b \geq 0$, then $b a \geq 0 \Rightarrow b R a$
For transitive :
If $a b \geq 0, b c \geq 0$, then also ac $\geq 0$ Relation $\mathrm{R}$ is reflexive, symmetric and transitive
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