PROBLEM 3. Given the set $S$ defined as follows
$S = \{1, 2, 3, 4, 5\}$
and the relation $R$ on $S$ defined as
$R = \{(1, 3), (3, 2), (4, 4), (5, 3)\}$
What points $(a, b) \in S \times S$ must be added to the relation $R$, in order for $R$ to be
(a) reflexive
(b) symmetric
(c) transitive
(d) symmetric and transitive