Home
Class 12
MATHS
Let R be the relation in the set Z of in...

Let R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0].

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

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Show that the relation R on the set Z of integers, given by R={(a ,\ b):2 divides a-b} , is an equivalence relation.

Let R be the relation in set N, given by R= {(a,b): a = b-2,b gt 6} . Then,

Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} given by R={(a ,\ b):2 divides (a-b)} . Write the equivalence class [0].

Let R be a relation on the set of integers given by aRb a= 2^k.b for some integer k. Then, R is

Let R be the equivalence relation in the set A={0,1,2,3,4,5} given by R={(a ,b): 2 \ d i v i d e s(a-b)} . Write the equivalence class [0].

Let R be the equivalence relation in the set A={0,1,2,3,4,5} given by R={(a ,b):2d i v i d e s(a-b)}dot Write the equivalence class [0].

check whether the relation R in the set N of natural numbers given by R = { (a,b) : a is divisor of b } is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a – b| is divisible by 2} is an equivalence relation. Write all the equivalence classes of R .

Let R be a relation from a set A to a set B, then

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. State the reason for the relation R on the set {1, 2, 3} given by R={(...

    Text Solution

    |

  2. Let R={(a ,\ a^3): a is a prime number less than 5} be a relation. Fin...

    Text Solution

    |

  3. Let R be the relation in the set Z of integers given by R={(a,b):2 div...

    Text Solution

    |

  4. For the set A={1,\ 2,\ 3} , define a relation R on the set A as follow...

    Text Solution

    |

  5. Let A={0,\ 1,\ 2,\ 3} and R be a relation on A defined as R={(0,\ 0),\...

    Text Solution

    |

  6. If the relation R be defined on the set A={1,2,3,4,5} by R={(a,b): |a^...

    Text Solution

    |

  7. Let the relation R be defined in N by aRb, if 2a + 3b = 30. Then R = …...

    Text Solution

    |

  8. Write the smallest equivalence relation on the set A={1,\ 2,\ 3} .

    Text Solution

    |

  9. Let R be a relation on the set N given by R={(a ,\ b): a=b-2,\ b >6}do...

    Text Solution

    |

  10. Which of the following is not an equivalence relation on Z ? a\ R\ b...

    Text Solution

    |

  11. R is a relation on the set Z of integers and it is given by (x ,\ y) i...

    Text Solution

    |

  12. Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the ...

    Text Solution

    |

  13. Let R be the relation over the set of all straight lines in a plane ...

    Text Solution

    |

  14. If A={a ,\ b ,\ c} , then the relation R={(b ,\ c)} on A is (a) reflex...

    Text Solution

    |

  15. Let A={2,\ 3,\ 4,\ 5,\ .......\ 17 ,\ 18} . Let ' ' be the equivalenc...

    Text Solution

    |

  16. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  17. The relation ' R ' in NxxN such that (a ,\ b)\ R\ (c ,\ d)hArra+d=b+c ...

    Text Solution

    |

  18. If A={1,\ 2,\ 3},\ \ B={1,\ 4,\ 6,\ 9} and R is a relation from A to B...

    Text Solution

    |

  19. A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x\ ...

    Text Solution

    |

  20. A relation varphi from C to R is defined by x\ varphi\ yhArr|x|=y . Wh...

    Text Solution

    |