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 !

The relation is on $N\times N$, so the reflexive property is that $(a,b)P(a,b)$. Can you show this? — Paulo Mourão, May 20 '19 at 19:04
when proving for transitive property , do we have to get , (a,b)P(c,d) and (c,d)P(e,f) — Lasan Manujitha Ukwaththa Liya, May 20 '19 at 19:08
You assume that and then aim to prove $(a,b)P(e,f)$. That proves the transitive property: $$(a,b)P(c,d)\quad\text{and}\quad(c,d)P(e,f) \implies(a,b)P(e,f)$$ — Paulo Mourão, May 20 '19 at 19:09
see similar thread https://math.stackexchange.com/q/21256/565609 — emonHR, May 20 '19 at 19:13

score 2 · Answer 1 · answered May 20 '19 at 19:03

2

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

answered May 20 '19 at 19:03

auscrypt

1 Answers1