Define an equivalence relation on $\{ 1,2,3,4 \}^2$ by: (, )(, ) if ⋅ = ⋅ . How many equivalence classes are there?

Question

I know that all the reflexive and symmetric pairs are part of this equivalence relation and I know that (2,2)(4,1) are in this equivalence relation as well. Im still not quit sure how to get to the answer..

Is there an algorithm to calculate the number of equivalence relation? and if there isn't, what is the best way to do it ? Any help is greatly appreciated.

Answer 1

Write down the $4 \times 4$ multiplication table (i.e. $i \times j$ for $1 \leq i,j \leq 4$). Each different value that turns up is an equivalence class, so count them.