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

  • TEST PAPER 1

    MODERN PUBLICATION|Exercise PROBLEM|75 Videos

  • TEST PAPER 2

    MODERN PUBLICATION|Exercise PROBLEM|74 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.

MODERN PUBLICATION-TEST PAPER 10-EXERCISE
  1. Solve x + 2y = 3, 3x + y = 4 by matrix method.

    Text Solution

    |

  2. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

    Text Solution

    |

  3. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

    Text Solution

    |

  4. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

    Text Solution

    |

  5. If x^7y^3=(x+y)^10, then find (d^2y)/(dx^2)

    Text Solution

    |

  6. If tangents are drawn from the origin to the curve y = sin x, then sho...

    Text Solution

    |

  7. Integrate the following int(3x+4)/(xsqrt(2x^2-5))dx

    Text Solution

    |

  8. Evaluate int(0)^(4)(x+e^(2x))dx, as limit of sum.

    Text Solution

    |

  9. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

    Text Solution

    |

  10. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

    Text Solution

    |

  11. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

    Text Solution

    |

  12. Prove that the lines joining the midpoints of consecutive sides of a q...

    Text Solution

    |

  13. int0^1(x^5(4-x^2))/sqrt(1-x^2)dx

    Text Solution

    |

  14. find the point of intersection of the line through (1,3,-2) and (3,4,1...

    Text Solution

    |

  15. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

    Text Solution

    |

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

    Text Solution

    |

  17. Show that f : A to B, where A=R - {3}, B=R - {1} defined as f(x)=(x-2)...

    Text Solution

    |

  18. Find the particular solution of the differential equation dy/dx+y cot ...

    Text Solution

    |

  19. Prove that the curves y^(2)=4x and x^(2)=4y divide the area of the squ...

    Text Solution

    |

  20. A line with direction ratios lt2,1,2gt meets each of the lines x=y+a=z...

    Text Solution

    |