The binary relation S = ∅ (empty set) on set A = {1, 2, 3} is:

The correct answer is Option D. A relation on A is reflexive only if every (a, a) is present for a ∈ A. Since S = ∅, none of (1,1), (2,2), or (3,3) is present, so S is not reflexive. For symmetry, the condition says that if (a, b) ∈ S, then (b, a) must also be in S; there is no pair in S that violates this, so S is symmetric vacuously. Similarly, transitivity requires that if (a, b) and (b, c) are in S, then (a, c) is in S; no such pair chain exists, so S is transitive vacuously.