what is meant by equivalent class

Asked by banga71 | 7th Apr, 2017, 10:05: PM

Expert Answer:

An equivalence class is defined as a subset of the form {x in X:xRa},
where a is an element of X and R is the equivalence relation between x and y.
Note that any two equivalence classes can either be either equal or disjoint,
Hence, the collection of equivalence classes forms a partition of X.

Consider the set,

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:
We could also define xRy iff xy(mod3), in which case our equivalence classes are:

Answered by Rebecca Fernandes | 27th Nov, 2017, 02:36: PM