Showing a relation in NxN is an equivalence relation, N denotes a set of positive integers

Question

Let $N∈Z^+$ and P represents a relation in$ N x N $defined by

$(a,b)P(c,d) $ iff $a + d = b + c$

we have to show that P is an equivalence relation

I tried to prove the reflexive property ,

then I'm confused whether to get $(a,a) or (a,b) $ ,

I can't find the head or tail of this question ,

can someone please explain clearly ,

Thank you so much !

Answer 1

The reflexive property is $(a,b)P(a,b)$. Does that clear it up?

Answer

This is equivalent to $a+b=a+b$ which is trivially true