I feel like I'm just being stupid and not seeing this problem properly, but I can't figure out how to do this question.
I know an equivalence relation is when a relation is transitive, reflexive, and symmetric.
Reflexive: I know this is true, but I'm not sure how to prove it in proper terms.
"When x is odd, and y=x, xRy because y must be odd as well, and when x=0, y=x, xRy. Thus, xRx."
Is that how you do it?
Symmetric: If xRy and x is odd, then y must be odd as well. Thus, yRx.
But what if x=0? Can't y be anything when x is zero, thus it isn't symmetric?
Transitive: Not sure how to prove this one either.
Equivalence class: I know that an equivalence class is the set of all numbers x in A so that for any given a, xRa. How do I find this for this problem?
Thanks in advance, I have an exam tomorrow so I could really use the help. This is from my study guide.