Thread: Proof of non-empty subsets, glb and lub

Let S be a non-empty subset of R and Suppose there is a non-empty set of T subset of S.
a) Prove: if S is bounded above, then T is bounded above and lub t< or = lub S.

b) Prove: if S is bounded below, then T is bounded below and glbT is > or = glbS.

I am having a really hard time with this.

a) if S is bounded above ---> exist supremum of S ---> that means that
sup( S ) >= every element of S and that means that sup( S ) >= every
element of T ( T is bounded above ) ---> exist supremum of T and sup( S ) >= sup( T )

b) look at a) part and you can figure it out