Problem 3 For each of the following, given an example of an order relation \le, a set X, and
a subset $A \subseteq X$ satisfying the statement, or otherwise, prove that there does not exist an
example that satisfies the statement.
(a) A has exactly two lower bounds, no infimum, 3 upper bounds, and no supremum.
(b) A has one lower bound and no infimum.