Check all properties that the following relations on the set of positive integers have. The relations are defined by (x, y)∈R if and only if the indicated condition is satisfied.

(a) x and y have a common prime factor

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

(b) x−y is a multiple of 3

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

(c) x and y are both prime

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

(d) x and y are twin primes (they are primes and their distance is 2)

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