Final answer:
An equivalence relation must be reflexive, symmetric, and transitive. None of the given options alone fulfill all three criteria, so the correct answer is '4) None of the above' because each property by itself does not constitute an equivalence relation.
Step-by-step explanation:
To determine which option represents an equivalence relation, we need to understand the properties that make up such a relation. An equivalence relation on a set is a relation that is reflexive, symmetric, and transitive. Therefore, for a relation to be an equivalence relation, it must satisfy all three of these properties.
- Reflexive: For every element 'a' in the set, the relation must include the pair (a, a).
- Symmetric: For every pair (a, b) in the relation, the pair (b, a) must also be in the relation.
- Transitive: For any three elements a, b, and c, if the relation includes the pairs (a, b) and (b, c), it must also include the pair (a, c).
Given that the domain is the set {1, 2, 3, 4}, the relation must exhibit reflexivity for each of those elements, symmetry for any pairs of elements, and transitivity across triples of elements. When we look at the given choices, we find that only Choice 1) Reflexive relation is potentially part of an equivalence relation, but a reflexive relation alone is not enough. We also require symmetry and transitivity.
In conclusion, the correct answer is 4) None of the above because none of the options represent a complete equivalence relation on their own. Each property is necessary, but not on its own sufficient, to constitute an equivalence relation.