4. (7 points) Consider the set $A=\{a,b,c,d,e\}$ and the relation $R$ on $A$ defined as follows: $R=\{(a,b),(b,c),(c,d),(d,e),(a,e)\}$.

(a) (1 point) Is $R$ reflexive?

(b) (1 point) Is $R$ symmetric?

(c) (1 point) Is $R$ transitive?

(d) (4 points) Does $R$ define a partial ordering? If not, what is the minimal number of ordered pairs that must be added to $R$ to make it a partial order?