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what is meant by equivalent class

Asked by banga71 7th April 2017, 10:05 PM
Answered by Expert
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 Expert 27th November 2017, 2:36 PM
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