Home
Class 12
MATHS
Let R be the relation on the set R of re...

Let R be the relation on the set R of real numbers such that aRb iff a-b is and integer. Test whether R is an equivalence relation. If so find the equivalence class of `1 "and" 1/2` wrt. This equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2018

    SHARAM PUBLICATION|Exercise EXERCISE|46 Videos
  • QUESTION PAPER 2020

    SHARAM PUBLICATION|Exercise EXERCISE|47 Videos

Similar Questions

Explore conceptually related problems

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.

Show that if R is an equivalence relation on X then dom R=rngR =X.

If R be a relation from the set A to the set B, then-

Let R be a relation in the set of natural numbers N defined by xRy if and only if x+y=18 . Is R an equivalence relation?

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

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

Show that the relation R is 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.

Show that if R is an equivalence relation on X, then Dom R = Rng R = X.

SHARAM PUBLICATION-QUESTION PAPER 2019-EXERCISE
  1. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

    Text Solution

    |

  2. Construct the multiplication table X7 on the set {1, 2, 3, 4, 5, 6}. A...

    Text Solution

    |

  3. Let R be the relation on the set R of real numbers such that aRb iff a...

    Text Solution

    |

  4. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

    Text Solution

    |

  5. Find the probability distribution of number of heads in three tosses...

    Text Solution

    |

  6. If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] then show that A^(3)-23A-40I=O

    Text Solution

    |

  7. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

    Text Solution

    |

  8. A person takes 4 tests in succession. The probability of his passing t...

    Text Solution

    |

  9. Find the point on the curve x^2 + y^2 - 4xy + 2 = 0 where the normal...

    Text Solution

    |

  10. Find the intervals in which the function y=(lnx)/(x) is increasing and...

    Text Solution

    |

  11. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

    Text Solution

    |

  12. Find (d^2y)/(dx^2) if x=a costheta,y=bsintheta.

    Text Solution

    |

  13. Verify lagrange's Mean-Value theorem for F(x) = x^3 - 2x^2 - x + 3 o...

    Text Solution

    |

  14. Find differential equation of the curve y=ae^(3x)+be^(5x).

    Text Solution

    |

  15. Obtain the general solution of the following differential equations. (...

    Text Solution

    |

  16. Evaluate : int0^(pi//2)(cosxdx)/((2-sinx)(3+sinx))

    Text Solution

    |

  17. Find the area of the region bounded by the curve y=6x-x^2 and the x-ax...

    Text Solution

    |

  18. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

    Text Solution

    |

  19. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

    Text Solution

    |

  20. Find a unit vector perpendicular to both of the vectors veca + vecb an...

    Text Solution

    |