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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 antisymmetricThe 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»

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.



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