Let $(A, \leq)$ be a poset and $B \subseteq A$. I need to show
i) B may have at most one least upper bound in A
ii) B may have at most one greatest lower bound in A.
This is really a matter of unpacking and applying the definitions of what it means
Recall the definition of a least upper bound as:
Let S be a poset:
A symmetrical definition defines the greatest lower bound.