Let `N` denote the set of all natural numbers and `R` be the relation on `N xx N` defined by `(a , b)R(c , d) iff a d(b+c)=b c(a+d)`. Check whether `R` is an equivalence relation on `N xx N`

Explanation

Here, `(a,b)R(c,d) <=> ad(b+c) = bc(a+d)` for all `(a,b),(c,d) in N xx N.`


First we will check `R` for reflexive.

For, `(a,b)R(a,b) `,

`=>ab(b+a) = ba(a+b)`, which is true.

So, `R` is reflexive.


Now, we will check `R` for symmetric.

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