Home
Class 11
MATHS
Let Z be the set of all integers and R b...

Let Z be the set of all integers and R be the relation on Z defined as `R = (a,b) : a,b `in` Z and a-b is divisible by 5) Prove that R is an equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|348 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

Similar Questions

Explore conceptually related problems

Let S be the set of all real numbers and let R be the relation in S defined by R = {(a,b), a leb^2 }, then

Show that relation R defined by R = {(a, b) : a - b is divisible by 3, a, binZ } is an equivalence relation.

Show that the relation R defined by : R = (a,b) : a-b is divisible by 3 a,b in N is an equivalence relation.

Show that the relation R defined by R = {(a, b) (a - b) , is divisible by 5, a, b in N} is an equivalence relation.

Show that the relation R defined by R = {(a, b): (a - b) is divisible by 3., a, b in N} is an equivalence relation.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxxNdot

If R is the relation in N xx N defined by (a, b) R (c,d) if and only if (a + d) =(b + c), show that R is an equivalence relation.

Let R be the relation on Z defined by : R ={(a,b) :a in Z,b in Z, a^2 =b^2} . Find : R.

Let N be the set of natural number and R be the relation in NxxN defined by : (a,b) R (c,d) iff ad = bc, for all (a,b), (c,d) in NxxN Show that R is an equivalence relation.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. Let Z be the set of all integers and R be the relation on Z defined as...

    Text Solution

    |

  2. If A = { a, b,c}, B = {p,q}, find BxxA .

    Text Solution

    |

  3. Let A = {1, 2, 3, 4,5,6} and B = {2,4,6, 8}. Find A xx B .

    Text Solution

    |

  4. Find x and y if : (x+1,y -2) = (3,1)

    Text Solution

    |

  5. Find x and y if : (x+ 2,4) = (5, 2x+ y)

    Text Solution

    |

  6. If (x/3+1, y-2/3)=(5/3, 1/3), find the values of x and y.

    Text Solution

    |

  7. Let A= {1, 2, 3,4} and S = {(a, b) : a in A, b in A, a divides b}. Wri...

    Text Solution

    |

  8. Let A = {1, 2} and B = {3, 4}. Write A xx B. How many subsets will A x...

    Text Solution

    |

  9. Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y...

    Text Solution

    |

  10. If the set A has 3 elements and the set B = {3, 4, 5}, then find the n...

    Text Solution

    |

  11. The Cartesian product A xx A has 9 elements among which are found (-1,...

    Text Solution

    |

  12. If A= {-1, 1}, find A xx A xx A.

    Text Solution

    |

  13. If R is the set of all real numbers. what do the cartesian products R ...

    Text Solution

    |

  14. If A xx B = {(a, x).(a , y). (b, x), (b, y)}. Find A and B.

    Text Solution

    |

  15. If A = { 1, 2}, B = {3, 4}, C = {4, 5}, find A xx (B uu C).

    Text Solution

    |

  16. If A={a, b,c}, B= {c, d} and C= {d, e, f}, find : (A nn B)xxC.

    Text Solution

    |

  17. If A={a, b,c}, B= {c, d} and C= {d, e, f}, find : (A xx B) nn (BxxC).

    Text Solution

    |

  18. Let A = {1, 2, 4}, B= {3, 5, 7} and C = {5, 7, 9}, find A xx (B nn C).

    Text Solution

    |

  19. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

    Text Solution

    |

  20. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

    Text Solution

    |

  21. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : Axx (B uu C).

    Text Solution

    |