2.	A relation  R is called Equivalence relation, if  it is 
a)	Reflexive, Symmetric and Transitive.   
b)	Reflexive, Anti symmetric  and Transitive.
c)	Symmetric and non- transitive
d)	None.


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.

A relation  R is called Equivalence relation, if it is a) Reflexive, Symmetric and Transitive. b) Reflexive, Anti symmetric and Transitive. c) Symmetric and non-transitive d) None.

Explore the properties of equivalence relations, including reflexivity, symmetry, and transitivity. This mathematical problem is suitable for high school students and dives into core concepts in set theory. Understand how relations partition sets into equivalence classes.

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