a) Prove that the relation R on the set N defined by;
aRb <-> a^2 - b^2 is divisible by 3
is an equivalence relation
b) Describe the partition induced by this relation R on the set N by this equivalence relation.
I don't know how to answer question b, could someone give me some insight as to how describe it.
I know how to work out part a, it is simply finding out whether it is reflexive, transitive and symmetric.
Could someone explain what partition means and how it fits in with this question.
I googled partitions and got something about parity, odd/even values and how they are partitions (classes) of N. That makes some sense but i cant relate it to this Q
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- Thread Starter
- 16-01-2010 17:03
- 16-01-2010 17:45
There's a theorem which says that any equivalence relation on a set partitions that set into things called 'equivalence classes'. A partition of a set X is a collection of pairwise disjoint sets A,B,C... such that the union of all the sets is X.