Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø Then (pick the TRUE statement)

R is symmetric and not transitive

R is symmetric and not transitive

Note here, it’s written that the relation is on collection of sets, i.e. the relation is between sets not between elements of sets. So, (A,B) will be part of R iff A∩B = ∅.



So it cant be reflexive since A∩A != ∅



But it can be symmetric since A∩B = B∩A = ∅ (here A and B are disjoint sets, A={1,2} and B={3,4}



Also, its not sure that it will always be transitive, for eg. A={1,2}, B={3,4} and C={2,5}, here A∩B = ∅, B∩C = ∅ but A∩C != ∅



which makes R, symmetric but not reflexive or transitive.