Given the following, I need to show that $\displaystyle sup S \leq inf T. $ Let S and T be nonempty subsets of $\displaystyle \mathbb{R} \backepsilon s \leq t \forall s \in S \wedge t \in t. $

A) Observe that S is bounded above and that T is bounded below.

B) Prove that $\displaystyle sup S \leq inf T. $

C) Given an example of such sets S and T where $\displaystyle S \cap T \neq \varnothing. $