Home
Class 12
MATHS
If R and S are transitive relations o...

If `R` and `S` are transitive relations on a set `A ,` then prove that `RuuS` may not be a transitive relation on `Adot`

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

Define a transitive relation.

Let R_1 and R_2 be equivalence relations on a set A, then R_1uuR_2 may or may not be

Let A={1,2,3} and R={(1,2),(1,1),(2,3)} be a relation on A . What minimum number of ordered pairs may be added to R so that it may become a transitive relation on Adot

If R and S are relations on a set A , then prove the following : R and S are symmetric RnnS and RuuS are symmetric R is reflexive and S is any relation RuuS is reflexive.

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

If R and S are relations on a set A , then prove the following: R and S are symmetric =>RnnS and RuuS are symmetric (ii) R is reflexive and S is any relation =>RuuS is reflexive.

If R and S are relations on a set A , then prove the following : (i) R and S are symmetric RnnS and RuuS are symmetric, (ii) R is reflexive and S is any relation RuuS is reflexive.

Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (1,\ 1),\ (2,\ 3)} be a relation on A . What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A .

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

Let R and S be two equivalence relations on a set A Then : A. R uu S is an equvalence relation on A B. R nn S is an equirvalenee relation on A C. R - S is an equivalence relation on A D. None of these

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. An integer m is said to be related to another integer n if m is a m...

    Text Solution

    |

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

    Text Solution

    |

  3. If R and S are transitive relations on a set A , then prove that...

    Text Solution

    |

  4. Let L be the set of all lines in X Y=p l a n e and R be the rela...

    Text Solution

    |

  5. Show that the relation geq on the set R of all real numbers is ref...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Let A={1,2,3}, and let R1="{"(1,1),(1,3),(3,1),(2,2")",(2,1),(3,3)}R2=...

    Text Solution

    |

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

    Text Solution

    |

  11. Is it true that every relation which is symmetric and transitive...

    Text Solution

    |

  12. Let A={1,2,3} and R={(1,2),(1,1),(2,3)} be a relation on A . What ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |