1. ## Equivalence Relation question

Let A = NxN, and define a relation R on A by (a,b)R(c,d) iff ab = cd.

I already proved that this is a relation.
But the question also asks to find the equivalence class E(9,2), and find an equivalence class with exactly 2 elements, one with 3 elements and one with 4 elements.
Im not sure how to do that with this question, or what that last part even means.

any help?

2. Originally Posted by p00ndawg
Let A = NxN, and define a relation R on A by (a,b)R(c,d) iff ab = cd.
But the question also asks to find the equivalence class E(9,2), and find an equivalence class with exactly 2 elements, one with 3 elements and one with 4 elements.
$E(9,2)=\{(9,2),(2,9),(1,18),(18,1),(3,6),(6,3)\}$

$E(1,2)=\{(1,2),(2,1)\}$

Now you finish.

3. just to make sure im understanding,

E(1, 4)= {3 elements} ??

4. Originally Posted by p00ndawg
just to make sure im understanding,

E(1, 4)= {3 elements} ??
What are the elements?

5. Originally Posted by plato
what are the elements?

(1,4), (4,1) (2,2)?

6. Originally Posted by p00ndawg
(1,4), (4,1) (2,2)?
Exactly.