Find whether or not `R_1={(1,\ 1),\ (1,\ 3),\ (3,\ 1),\ (2,\ 2),\ (2,\ 1),\ ` `(3,\ 3)}` , on `A={1,\ 2,\ 3}` is (i) reflexive (ii) symmetric (iii) transitive.

Explanation

Given set is `A=\{1,2,3\}`

and the relation is `R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}`

Let `A` be a set in which the relation `R` defined.

1.R is said to be a Reflexive Relation `(a, a) \in R`

2. `R` is said to be a symmetric relation, if `(a, b) \in R \Rightarrow(b, a) \in R`

3. `R` is said to be a transitive relation, if `(a, b) \in R,(b, c) \in R \Rightarrow(a, c) \in R`

Since, `1,2,3 \in A` and `(1,1),(2,2),(3,3) \in R`

`\Rightarrow` Every element maps to itself.

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