Let X and Y be nonempty bounded subsets of , where = Sup X and =Sup(Y). Let Z ={ }. show by example that Sup(Z) in general.

I was thinking of letting Sup(X) = = 4 and Sup(Y) = =-3

then I would have , therefore the Sup(Z) would have to be greater then -12 in order for the statement to be true, thus the inequality holds. Is this a correct assumption?