what is meant by equivalent class

An equivalence class is defined as a subset of the form ,

where a is an element of  and R is the equivalence relation between  and .

Note that any two equivalence classes can either be either equal or disjoint,

Hence, the collection of equivalence classes forms a partition of .

 

Example:

Consider the set, S ={0,1,2,3,4,5} There are many equivalence relations we could define on this set. One would be xRy iff x=y, in which case the equivalence classes are: [0]={0}  [1]={1} . . . . . [5]={5} We could also define xRy iff x≡y(mod3), in which case our equivalence classes are: [0]=[3]={0,3} [1]=[4]={1,4} [2]=[5]={2,5}