Three relations `R_1, R_2a n dR_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

(i) first check for `R_1`​

Reflexive `:(a,a), (b,b), (c,c)∈R`

Not symmetric `:(a,b) ∈R` but
`(b,a)∈/R1​`

Transitive `(a,b) ∈R, (b,c) in R_1​`

`=> (a,c) ∈R_1​`

(ii) For `R_2`

​ Not reflexive `(a,a) ∈R`

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