Equivalence Relation Proof

So, here is the question:

"Suppose ~ is a relation on A that is reflexive and has the property that for all elements a, b, and c in A, if a~b and a~c, then b~c. Prove that ~ is an equivalence relation on A."

This is from Keef and Guichard's "An Introduction to Higher Mathematics," through which I am trying to slog right now (see link for PDF: http://people.whitman.edu/~gordon/higher_math.pdf).

On the text's p. 27 in ch. 1.7, #5 (written out above) is currently stumping the hell out of me. I know that Reflexivity is obviously given, but I don't know how to pull out Symmetry and Transitivity from the rest of the problem.

Can someone please help me? Thanks!

Re: Equivalence Relation Proof

Re: Equivalence Relation Proof

Quote:

Originally Posted by

**dpmagee10** "Suppose ~ is a relation on A that is reflexive and has the property that for all elements a, b, and c in A, if a~b and a~c, then b~c. Prove that ~ is an equivalence relation on A."

Relations satisfying the property above are sometimes called Euclidean.