0
$\begingroup$

I have the relation congruent modulo 3 on the set $A=\{0,1,2,3,4,5\}$ and I have to find all of the equivalence classes for each element of $x$ of $A$.

I saw a different post where they split the set into three classes: one where the elements are divisible by 3, one where the elements have a remainder of 1, and one where the elements have a remainder of 2.

So basically $A_{0}=\{{0,3}\}$ and $A_{1}=\{{1,4}\}$ and $A_{2}=\{{2,5}\}$.

I don't really get how they decided to split the set up like this and also how to figure out what [0],[1],[2],...,[5] is for this. Also does this mean that some of the equivalence classes between 0 and 5 are equal?

  • 0
    Equivalence classes may have different representatives. For instance $[0]=[3]$ are two names for $A_0$. – 2017-02-21
  • 0
    if there are only 3 equivalence classes, does that mean that [1]=[4] and [2]=[5]? – 2017-02-21
  • 0
    In this case, yes. $[1] = [4] = A_1$ and $[2]=[5]=A_3$. – 2017-02-21

0 Answers 0