So there are a few questions that go along with this but I've hopefully worked them out correctly so I am only posting the ones I definitely have no clue about.

Let A be a bounded set of reals and z a real number such that the following holds: For every ε>0 there is an a∈A such that a<z+ε (if it is true, prove it. If not, then show a counterexample.

(1) inf A $\displaystyle \leq$ z

I said it was TRUE but I don't know how I would prove it.

(2) inf A $\displaystyle \geq$ z

This one I have no clue about. I'm assuming its FALSE because I said the above statement is true.

(3) sup A $\displaystyle \leq$ z

I said True by trichotomy..but I know that isn't a proof so how would I prove this one as well.

Thanks!