You're getting confused because the set in this question is a set of ordered pairs of real numbers (rather than single numbers) and you're confusing the individual numbers in an ordered pair with two ordered pairs that may or may not be related. (Sorry if that sentence sounds complicated!)
So let me try and simplify it for you. Take the first claim, and represent the ordered pair by , and the second ordered pair by . Then if you're going to decide whether or not the relation is symmetric, you must decide whether . Can you now see that this has nothing to do with ? So the answer to the first question is F - the proof is wrong.
Now apply the same thinking to the second question. Does ? Yes, and the proof is correct, because . So the grade is A (correct).