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Three relations R1, R2a n dR3 are define...

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.

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Show that the relation R defined by R={(a , b):a-b is divisible ...

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  2. Prove that a relation R on a set A is symmetric iff R=R^-1

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  3. Three relations R1, R2a n dR3 are defined on set A={a , b , c} as foll...

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  4. Let a relation R1 on the set R of real numbers be defined as (a , b) ...

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  5. Let S be the set of all points in a plane and R be a relation on S def...

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  6. The following relation is defined on the set of real number: a R ...

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  7. Prove that every identity relation on a set is reflexive, but the c...

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  8. Let R be a relation defined on the set of natural numbers N as R={(...

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  9. Let N denote the set of all natural numbers and R be the relation on N...

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  10. Let N be the set of all natural numbers and let R be a relation on N×N...

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  11. Let R be a relation on the set of all line in a plane defined by (l1, ...

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  12. Each of the following defines a relation on N:x -> y , (i) x , y in N...

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  13. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

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  14. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

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  15. Let A={1,2,3,ddot,9} and R be the relation in AxA defined by (a ,b)R(c...

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  16. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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  17. Let n be a positive integer. Prove that the relation R on the set Z o...

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  18. Let "T" be the set of all triangles in a plane with "R" as relation ...

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  19. If R and S are relations on a set A , then prove the following : (...

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  20. Let S be a relation on the set R of all real numbers defined by S=...

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