Given the following relations on the set of all people. Check ALL correct answers from the following lists:

(a) $a$ is older than $b$

A. antisymmetric
B. irreflexive
C. transitive
D. reflexive
E. symmetric

(b) $a$ and $b$ have a common grandparent

A. antisymmetric
B. symmetric
C. transitive
D. reflexive
E. irreflexive

(c) $a$ has the same first name as $b$

A. irreflexive
B. transitive
C. symmetric
D. antisymmetric
E. reflexive

(d) $a$ and $b$ were born on the same day

A. symmetric
B. transitive
C. reflexive
D. irreflexive
E. antisymmetric