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 xv = yu. Show that R is an equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 6

    MODERN PUBLICATION|Exercise EXERCISE|43 Videos

  • TEST PAPER 8

    MODERN PUBLICATION|Exercise EXERCISE|40 Videos

Similar Questions

Explore conceptually related problems

Let R={(m,n):2 divides m+n} on Z. Show that R is an equivalence relation on Z.

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

Let ~ be defined by (m,n)~(p,q) if mq=np where m, n, p, qinZ -{0}. Show that it is an equivalence relation.

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

If N denotes the set of all natural numbers and R be the relation on N xx N defined by (a, b) R (c, d) if ad(b+ c)=bc(a+d) . Show that R is an equivalence relation.

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?

Let n be a fixed positive integer. Define a relation R on Z as follows for all a, b in Z, aRb, if and only if a-bis divisible by n. Show that R is an equivalence relation.

If Z is the set of all integers and R is the relation on Z defined as R={(a, b): a, b in Z and a-b is divisible by 3. Prove that R is an equivalence relation.

Let A={1,2,3,...,9) and R be the relation on A xx A defined by (a, b) R (c,d), if a+d=b+c for (a, b), (c,d) in A xx A. Prove that R is an equivalence relation and also obtain the equivalence class (2,5).

If A = {1,2,3,…,9} and R is the relation in A xx A defined by (a, b) R (c, d), if a+d=b+c for (a, b), (c, d) in A xx A . Prove that R is an equivalence relation.

MODERN PUBLICATION-TEST PAPER 7-EXERCISE
  1. Let A = R-{2} and B = R - {1}. If f : A rarr B is a function defined b...

    Text Solution

    |

  2. Given a non-empty set X, Let *: P(x) xx P(x) be defined as A**B =(A-B...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. An animal feed company must produce 200kg of a mixture consisting of i...

    Text Solution

    |

  6. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|=abc(1+1/a+1/b+1/c)or(ab...

    Text Solution

    |

  7. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

    Text Solution

    |

  8. Express as a sum of a symmetric and a skew symmetric matrix: [[x,a,b],...

    Text Solution

    |

  9. Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,c...

    Text Solution

    |

  10. Test differentiability of the following function at the indicated poin...

    Text Solution

    |

  11. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

    Text Solution

    |

  12. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

    Text Solution

    |

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

    Text Solution

    |

  14. Test the function y = (x - 5)^5( x + 2)^2 for extreme values.

    Text Solution

    |

  15. Evaluate : int ((sinxcosx)/(sin2x) - 2sinx+3)dx .

    Text Solution

    |

  16. int0^(pi/2)(cosxdx)/((sinx+1)(sinx+2))

    Text Solution

    |

  17. Solve : (x + 2y^3)dy/dx = y.

    Text Solution

    |

  18. Find the general solution of dy/(du) = u+1/sqrtu + 6u + 5.

    Text Solution

    |

  19. Prove the following by vector method. The diagonals of a rhombus are a...

    Text Solution

    |

  20. Find the equation of the plane passing through the line of intersectio...

    Text Solution

    |