If the relation ~ on NxN holds by the rule (a,b)~(c,d) <=> a+d = b+c, then prove that ~ is an equivalence relation.

I know that an equivalence relation is one that is reflexive, symmetric and transitive so then i have to prove all three on the rule above..

So if a,d are elements of N then a+d=d+a

Similiarly if b,c are elements of N then b+c=c+b

Thus (a,b) ~(c,d) are reflexive.

Is this correct?

If a = b and b=a then a~b

If c=d and d=c then c~d

Therefore (a,b) ~ (c,d) is symmetric.

Is this correct?

As for transitivity, i dont know...

any help is welcome!

zee