Relation S is defined as a set in which no element of A is related to any element.
This means that R is an empty relation.
Empty relation with empty set holds Reflexivity, Transitivity, Symmetric, Anti-Symmetric
This empty relation would match all conditions vacuously because there are no conditions to check(no elements)
Empty relation with non-empty set holds Transitivity, Symmetric, Anti-Symmetric but not reflexivity because set is non-empty and there are conditions to check for reflexive property.
In this particular question set A is non empty hence answer is D) Transitive and symmetric