Home
Class 12
MATHS
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.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|449 Videos

  • SCALAR OR DOT PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|233 Videos

Similar Questions

Explore conceptually related problems

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.

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

R_2={(a ,\ a)} is defined on set A={a ,\ b ,\ c} . Find whether or not it is (i) reflexive (ii) symmetric (iii) transitive.

Let a = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c), (a, b)} be a relation on A, then the

Let R be a relation on A = {a, b, c} such that R = {(a, a), (b, b), (c, c)}, then R is

Find which of the following are the function on set A={a,b,c} ? Give reason. (i) R_(1)={(a,b),(b,a),(a,c)} (ii) R_(2)={(b,b),(c,c),(a,b)}

Let R={(a ,\ a),\ (b ,\ b),\ (c ,\ c),\ (a ,\ b)} be a relation on set A={a ,\ b ,\ c} . Then, R is (a) identity relation (b) reflexive (c) symmetric (d) equivalence

If A={a,b,c} , then the relation R={(a,b),(b,a)} is:

If A={a ,\ b ,\ c ,\ d}, then a relation R={(a ,\ b),\ (b ,\ a),\ (a ,\ a)} on A is (a)symmetric and transitive only (b)reflexive and transitive only (c) symmetric only (d) transitive only

Let R be a relation in N defined by R={(a , b); a , b in N\ a n d\ a=b^2dot} Are the following true: (i)\ (a , a) in R\ AA\ a in N (ii)\ (a , b) in R=>(b , a) in R (iii)\ (a , b) in R ,(b , c) in R=>(a , c) in R

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

    Text Solution

    |

  2. Test whether the following relations R1,R2"and"R3,"" are (i) reflex...

    Text Solution

    |

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

    Text Solution

    |

  4. Show that the relation R on the set A{xZ ;0lt=12}, given by R={(a ,...

    Text Solution

    |

  5. Let n be a fixed positive integer. Define a relation R on Z as f...

    Text Solution

    |

  6. Let Z be the set of all integers and Z0 be the set of all non zero...

    Text Solution

    |

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

    Text Solution

    |

  8. If R is an equivalence relation on a set A, then R^-1 is

    Text Solution

    |

  9. On the set N of all natural numbers, a relation R is defined as follow...

    Text Solution

    |

  10. If R1 and R2 are equivalence relations in a set A, show that R1nnR2...

    Text Solution

    |

  11. Let Z be the set of all integers and Z0 be the set of all non-zero...

    Text Solution

    |

  12. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given b...

    Text Solution

    |

  13. An integer m is said to be related to another integer n if m is a mult...

    Text Solution

    |

  14. Show that the relation geq on the set R of all real numbers is r...

    Text Solution

    |

  15. m is said to be related to n if m and n are integers and m-n is divisi...

    Text Solution

    |

  16. Let O be the origin. We define a relation between two points P and ...

    Text Solution

    |

  17. Show that the relation R defined by R={(a , b):a-b is divisible ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |