`R_1={(a ,\ a),\ (a ,\ b),\ (a ,\ c),\ (b ,\ b),\ (b ,\ c),\ (c ,\ a),\ (c ,\ b),\ (c ,\ c)}` is defined on set `A={a ,\ b ,\ c}` . Find whether or not it is (i) reflexive (ii) symmetric (iii) transitive.

Explanation

We have set,

`A=\{a, b, c\}`


Here, `R_{1}, R_{2}, R_{3}`, and `R_{4}` are the binary relations on set `A`.


So, recall that for any binary relation `R` on set `A`. We have,

`R` is reflexive if for all `x \in A, x R x`.

(ii). Symmetric:

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