I understand for the most part the conceptual aspects of an equivalence relation. A relation is considered a equivalence relation if it satisfies reflexive, symmetric and transitive properties but Im having trouble working with this on paper.
For example, Given a relation R defined on the integers by aRb <=> a+b is even, show that this relation is an equivalence relation.
So far my approach is. Reflexive, aRa <=> a+a is even Symmetric, if bRa <=> b+a is even Transitive, if aRb and bRc then aRc <=>a+c is even.
But after that i am stuck.
Just apply the definition :
reflexivity : $a+a = 2 a$ is even, so $aRa$
symetric : if $aRb$ then a+b is even, then b+a is even then $bRa$
transitive : if $aRb$ and $bRc$ then a+b is even and b+c is even, then a+2b+c is even then a+c is even (because 2b is even), then $aRc$