Equivalence relation

[reddog843]

I am really confused by this one so any help would be great.

P is a preorder for a set A if P is a reflexive and transitive relation on A. Define a relation E on A by xEy iff xPy and yPx.
Show that E is an equivalence relation on A.

Thanks!!

[OfficeShredder]

You need to show three things (by definition of an equivalence relation):

xEx
xEy <--> yEx
xEy and yEz --> xEz


So try literally applying the definition of E to the situations described above, and see if you can prove them