relation on A that is symmetric and transitive but not reflexive

[Easy_as_Pi]

Homework Statement

Let A = {1,2,3,4}. Give an example of a relation on A that is symmetric and transitive, but not reflexive.

Homework Equations

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

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?

 

[jgens]

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

 

[Easy_as_Pi]

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