Final answer:
An equivalence relation requires a relation to be reflexive, symmetric, and transitive. None of the options provided singly fulfills all these requirements, hence the correct answer is 4) None of the above for the domain set {1, 2, 3, 4}.
Step-by-step explanation:
To determine which relation is an equivalence relation for the domain set {1, 2, 3, 4}, let's review the properties that define an equivalence relation. An equivalence relation is one that is reflexive, symmetric, and transitive. These are three necessary properties:
- Reflexive: Every element is related to itself. For example, in the set {1, 2, 3, 4}, (1,1), (2,2), (3,3), and (4,4) would be in the relation.
- Symmetric: If (a, b) is in the relation, then (b, a) is also in the relation.
- Transitive: If (a, b) and (b, c) are in the relation, then (a, c) must also be in the relation.
Based on the provided options, the relation that is an equivalence relation must satisfy all three properties, not just one. Therefore, the correct answer is option 4) None of the above. A relation can't be an equivalence relation unless it is reflexive, symmetric, and transitive.