Show that if A= { 1,2,3} and R ={(1,1),(2,2),(3,3) (1,2),(2,1),(2,3),(1,3) is an equivalence relation.

Explanation

To show that the relation \( R \) on the set \( A = \{1, 2, 3\} \) is an equivalence relation, we need to verify that \( R \) is reflexive, symmetric, and transitive.

### Step 1: Check Reflexivity
A relation \( R \) is reflexive if every element in \( A \) is related to itself. This means for every \( a \in A \), the pair \( (a, a) \) must be in \( R \).

- For \( a = 1 \): \( (1, 1) \in R \)
- For \( a = 2 \): \( (2, 2) \in R \)
- For \( a = 3 \): \( (3, 3) \in R \)
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