Let N be the set of all natural numbers and let R be a relation on `N×N` , defined by `(a , b)R(c , d) iff a d=b c` for all `(a , b),(c , d) in N × Ndot` . Show that `R` is an equivalence relation on `N × N` .

Explanation

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


First we will check `R` for reflexive.

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

`=>ab = ba`, which is true.

So, `R` is reflexive.


Now, we will check for symmetric.

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