Need help on another proof

Hello thanks for everyone who helped me on the previous implication proof, here's another problem I'm stuck on:

(Prove or disprove)

http://imgur.com/14PMD.jpg

I think it has something to do with x^2 - y^2 = (x + y)(x - y), and here's my interpretation of "i)":

For every real x and positive real e, there exists one or more positive real delta so that if |x - y| is smaller than delta then |x^2 - y^2| must be smaller than e, which works for any real y.

But I'm lost at where to go next, since delta could be any number, and with the absolute sign there won't be negative numbers. The same thing with "ii)" and "iii)", where "ii)" simply switched the ordering of the sets and "iii)" limits x and y to 1 and 2.

Thanks for any help!