The correct answer is:

a) Reflexive, Symmetric, and Transitive.

Explanation:

An equivalence relation on a set is defined as a relation that satisfies three key properties:

1. Reflexive: Every element is related to itself. For all $a \in A$, $aRa$.
2. Symmetric: If one element is related to another, then the second element is related to the first. For all $a, b \in A$, if $aRb$, then $bRa$.
3. Transitive: If an element is related to a second one, and that second one is related to a third, then the first element is related to the third. For all $a, b, c \in A$, if $aRb$ and $bRc$, then $aRc$.

Would you like more details on how these properties work or examples of equivalence relations?

Relative Questions:

1. What is an example of an equivalence relation?
2. How do you determine if a relation is reflexive?
3. What is the difference between symmetric and antisymmetric relations?
4. Can a relation be transitive but not symmetric?
5. What are some real-world examples of equivalence relations?

Tip:

Equivalence relations partition a set into disjoint equivalence classes, where every element in a class is related to each other under the relation.