Home
Class 12
MATHS
Let R be a relation on the set A of orde...

Let R be a relation on the set A of ordered pairs of positive integers defined by `(x , y)"R"(u , v)` if and only if `x v=y u` . Show that R is an equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA ENGLISH|Exercise All Questions|90 Videos
  • HIGHER ORDER DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|179 Videos

Similar Questions

Explore conceptually related problems

Let R be a relation on the set A of ordered pairs of integers defined by (x ,\ y)\ R\ (u ,\ v) iff x v=y udot Show that R is an equivalence relation.

Let R be a relation on the set of all real numbers defined by xRy iff |x-y|leq1/2 Then R is

A relation R on the set of complex numbers is defined by z_1 R z_2 if and only if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let n be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by (x , y) in R iff x-y is divisible by n , is an equivalence relation on Z.

Let m be a given fixed positive integer. Let R={(a.b) : a,b in Z and (a-b) is divisible by m} . Show that R is an equivalence relation on Z .

Let R be a relation on the set of all lines in a plane defined by (l_1,\ l_2) in R line l_1 is parallel to line l_2 . Show that R is an equivalence relation.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let R be a relation on N defined by x+2y=8. The domain of R is

RD SHARMA ENGLISH-FUNCTION-All Questions
  1. Let A={x in R :0lt=xlt=1}dot If f: A->A is defined by f(x)={(x ,, if ...

    Text Solution

    |

  2. Let A=[-1,1]dot Then, discuss whether the following functions from A t...

    Text Solution

    |

  3. Let R be a relation on the set A of ordered pairs of positive intege...

    Text Solution

    |

  4. Let A be a finite set. If f: AvecA is an onto function, show that f is...

    Text Solution

    |

  5. Show that the function f: R-{3}->R-{1} given by f(x)=(x-2)/(x-3) is ...

    Text Solution

    |

  6. Show that the function f: Rvec R given by f(x)=x^3+x is a bijection.

    Text Solution

    |

  7. Let f: Nuu{0}->Nuu{0} be defined by f={(n+1 ,, ifn \ i s \ e v e n),(n...

    Text Solution

    |

  8. Let f: N-[1]vecN be defined by, f(n)= the highest prime factor ofn . S...

    Text Solution

    |

  9. Let A={1,2} . Find all one-to-one function from A to A.

    Text Solution

    |

  10. Let f: Rveca n dg: RvecR be defined by f(x)=x+1a n dg(x)=x-1. Show tha...

    Text Solution

    |

  11. Verify assoiativity for the following three mappings : f: N->Z0 (t...

    Text Solution

    |

  12. If the set A contains 5 elements and the set B contains 6 elements, th...

    Text Solution

    |

  13. If the set A contains 7 elements and the set B contains 10 elements, ...

    Text Solution

    |

  14. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

    Text Solution

    |

  15. The inverse of the function f: Rvec{x in R : x<1} given by f(x)=(e^x-...

    Text Solution

    |

  16. Let A={1,2,3}dot Write all one-one from A to itself.

    Text Solution

    |

  17. If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a b...

    Text Solution

    |

  18. If the function f:[1,oo)->[1,oo) is defined by f(x)=2^(x(x-1)), then ...

    Text Solution

    |

  19. The value of parameter alpha, for which the function f(x) = 1+alpha x,...

    Text Solution

    |

  20. Let R^+ be the set of all non-negative real numbers. if f: R^+ rar...

    Text Solution

    |