If P is a partition of A then the relation R defined by aRb if a and b are in the same set of P is an equivalence relation on A.

Question

anonymous · Answer

Do you know they three things you need to show in order for the relation R to be an equivalence relation?

anonymous · Answer

aRa, aRb = bRa, and aRb, bRc, then aRc

anonymous · Answer

Right. Lets do each separately. 

Does aRa for all a in A?  In other words, are a and a both in the same set of the partition P for any a in A?

anonymous · Answer

yeah

anonymous · Answer

oh nevermind it's kind of easy then, because R is a relation for elements in the same partition, so aRb would means bRa and then the third one would be easy as well

anonymous · Answer

Yeah, its pretty straight  forward.

anonymous · Answer

In fact, some books take that to be the definition of an equivalence relation.