The binary relation S = ϕ (empty set) on set A = {1, 2, 3} is:
2002
The binary relation S = ϕ (empty set) on set A = {1, 2, 3} is:
Answer: D. Transitive and symmetric — An empty relation on a non-empty set is never reflexive because it lacks pairs (a, a) for elements in A. However, symmetry and transitivity hold vacuously…
- A.
Neither reflexive nor symmetric
- B.
Symmetric and reflexive
- C.
Transitive and reflexive
- D.
Transitive and symmetric
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Correct answer: D
An empty relation on a non-empty set is never reflexive because it lacks pairs (a, a) for elements in A. However, symmetry and transitivity hold vacuously since there are no pairs to violate these conditions. Therefore, the relation is symmetric and transitive.
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