1. ## Relations

Let m, n be integers. A relation Rm,n on Z is defined as follows: for a, b ∈ Z, if
there exists an integer k such that ma + nb = (m + n)k, then (a, b) ∈ Rm,n.
(a) Prove Rm,n is an equivalence relation.
(b) Write down a quotient set for R3,1.

2. Originally Posted by modi4help
Let m, n be integers. A relation Rm,n on Z is defined as follows: for a, b ∈ Z, if
there exists an integer k such that ma + nb = (m + n)k, then (a, b) ∈ Rm,n.
(a) Prove Rm,n is an equivalence relation.
(b) Write down a quotient set for R3,1.
How far have you gone in proving this for yourself?
Where are you are having trouble?

3. I didn't know how to start solving it properly.

4. Originally Posted by modi4help
I didn't know how to start solving it properly.
start with part (a). what does it mean to be an equivalence relation? hence, what do you need to show to prove that we have an equivalence relation?

5. Originally Posted by modi4help
Let m, n be integers. A relation Rm,n on Z is defined as follows: for a, b ∈ Z, if
there exists an integer k such that ma + nb = (m + n)k, then (a, b) ∈ Rm,n.
(a) Prove Rm,n is an equivalence relation.
(b) Write down a quotient set for R3,1.