"Let $\mathrm{R}$ be a relation on $\mathrm{N} \times \mathbb{N}$ defined by $(a, b) ~\mathrm{R}~(c, d)$ if and only if $a d(b-c)=b c(a-d)$. Then $\mathrm{R}$ is"

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Accepted Answer

"Given, $(a, b) R(c, d) \Rightarrow a d(b-c)=b c(a-d)$

Symmetric :

(c, d) $R(a, b) \Rightarrow \operatorname{cb}(\mathrm{d}-\mathrm{a})=\mathrm{da}(\mathrm{c}-\mathrm{b}) $

$\Rightarrow$ Symmetric.

Reflexive :

(a, b) R (a, b) $\Rightarrow a b(b-a) \neq b a(a-b) $

$\Rightarrow$ Not reflexive.

Transitive :

$(2,3) \mathrm{R}(3,2)$ and $(3,2) \mathrm{R}(5,30)$ but

$((2,3),(5,30)) \notin \mathrm{R} $

$\Rightarrow$ Not transitive."

Let $\mathrm{R}$ be a relation on $\mathrm{N} \times \mathbb{N}$ defined by $(a, b) ~\mathrm{R}~(c, d)$ if and only if $a d(b-c)=b c(a-d)$. Then $\mathrm{R}$ is

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Let $\mathrm{R}$ be a relation on $\mathrm{N} \times \mathbb{N}$ defined by $(a, b) ~\mathrm{R}~(c, d)$ if and only if $a d(b-c)=b c(a-d)$. Then $\mathrm{R}$ is

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