Homework Help: [Solved] relation on A that is symmetric and transitive but not reflexive

1. Dec 1, 2011

Easy_as_Pi

1. The problem statement, all variables and given/known data
Let A = {1,2,3,4}. Give an example of a relation on A that is symmetric and transitive, but not reflexive.

2. Relevant equations
Symmetric: if aRb then bRa
Transitive: if aRb and bRc then aRc
Reflexive: aRa for all a in A

3. The attempt at a solution
{(1,2),(2,1),(1,1)} It's symmetric because 1R2 and 2R1. Not reflexive because (2,2)...(4,4) are not elements and transitive because 1R2 and 2R1 so 1R1. Yet, this one got marked wrong on my homework. I'm going to assume my teacher is right, and I'm wrong. Can anyone find my mistake?

Last edited: Dec 1, 2011
2. Dec 1, 2011

jgens

Re: Give an example of a relation on A that is symmetric and transitive but not refle

2R1 and 1R2 implies 2R2 if your relation is transitive. But (2,2) isn't in A. So your teacher is right.

3. Dec 1, 2011

Easy_as_Pi

Re: Give an example of a relation on A that is symmetric and transitive but not refle

Oh wow, I can't believe I missed that! Thanks for that!