Three relations `R_1, R_2 and R_3` are defined on set `A={a , b , c}` as follow:
`R_1={(a , a),(a , b),(a , c),(b , b),(b , c),(c , a),(c , b),(c , c)}`
`R_2={(a , b),(b , a),(a , c),(c , a)}`
`R_3={(a , b),(b , c),(c , a)}`
Find whether each of `R_1, R_2,R_3` is reflexive, symmetric and transitive.

Explanation

To determine whether the relations \( R_1, R_2, \) and \( R_3 \) are reflexive, symmetric, and transitive, we will analyze each relation step by step.

### Step 1: Check Reflexivity

A relation \( R \) on a set \( A \) is reflexive if every element in \( A \) is related to itself. This means for all \( x \in A \), the pair \( (x, x) \) must be in \( R \).

**Set \( A = \{a, b, c\} \)**

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