b) and c) are symmetric because when the relation is true for one, the reverse is also true

i.e if a born on the same day as b then the reverse: b is born on the same day as a is also true

a) Is anti-symmetric because when the relation is true for 1 the opposite of the reverse of the relation is true.

Height_a > Height_b is true

The reverse is Height_b > Height_a

The opposite of the reverse Height_b < Height_a is true