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Three relations `R_1, R_2` and `R_3` are defined on a set `A ={a, b, c}`: as for `R_1 = {(a, a), (a, b), (a, c), (b, b), (b, c), (c, a), (c, b), (c c)}` (a Find whether or not each of the relations R1,is Symmetric , reflexive or transitive. |
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Answer» `R_1 = {(a,a),(a,b),(a,c),(b,b),(b,c),(c,a),(c,b),(c,c)}` As `R_1` contains `(a,a),(b,b) and (c,c)`, so, it is reflexive. As `R_1` contains `(a,b)` but do not contain `(b,a)`, so it is not symmetric. As `R_1` contains `(a,b),(b,c)` and `(a,c)`, so it is transitive. `R_2 = {(a,a)}` As `R_2` contains `(a,a)`,but, do not contain `(b,b) and (c,c)`, so, it is not reflexive. As `R_2` do not contain `(a,b)` and `(b,a)`, so it is not symmetric. Also, `R_2` is not transitive. `R_3 = {(b,c)}` Based on the above explanation, `R_3` is not symmetric, reflexive and transitive. |
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