Let [R] be a relation on [N N] defined by [(a, b) ~R~(c, d)] if and only if a d(b-c)=b c(a…

Question

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

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) 
eq 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)) 
otin \mathrm{R} $

$\Rightarrow$ Not transitive.

Solutions · 1