Question

The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________

(a) reflective, symmetric and transitive

(b) irreflexive, symmetric and transitive

(c) neither reflective, nor irreflexive but transitive

(d) irreflexive and antisymmetric

The question was posed to me at a job interview.

I want to ask this question from Types of Relations topic in chapter Relations of Discrete Mathematics

Answer 1

The correct option is (c) neither reflective, nor irreflexive but transitive

To explain I would say: Not reflexive -> (3,3) not present; not irreflexive -> (1, 1) is present; not symmetric -> (2, 1) is present but not (1, 2); not antisymmetric – (2, 3) and (3, 2) are present; not asymmetric -> asymmetry requires both antisymmetry and irreflexivity. So, it is transitive closure of relation.