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.

  • $\begingroup$ You have the right definitions, now you need to apply them. For example, for reflexivity, as you wrote aRa <=> a+a is even. If a is an integer, can you see why a+a will always be even? The other properties are done similarly. $\endgroup$ – pwerth Mar 5 '15 at 4:03

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 $aRc$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.