Option B: $R$ 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.