Home
Class 12
MATHS
Show that the relation R on the set N x...

Show that the relation `R` on the set `N xx N` defined by `(a, b)R(c, d)` iff `a d(b+c)=b c(a+d)` is an equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|132 Videos

  • THREE DIMENSIONAL GEOMETRY

    V PUBLICATION|Exercise QUESTION BANK|103 Videos

Similar Questions

Explore conceptually related problems

Show that the relation R on the set of natural numbers defined as R:{(x,y):y-x is a multiple of 2} is an equivalance relation

Show that each of the relation R in the set A={x in Z: 0lt= xlt=12} ,given by R = {(a,b) : a=b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Show that the relation R in the set is given by A={x in Z,0lexle12} R={(a,b):a-b is a multiple of 4} is an equivalence relation.

Show that each of the relation R in the set A={x in Z: 0 le xle12} ,given by R = {(a,b) : |a-b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1 in each case.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find R.

Show that the relation R in the set R of real number, defined as R = {(a.b): a lt= b^2} is neither reflexive nor symmetric nor transitive.

V PUBLICATION-RELATIONS AND FUNCTIONS-QUESTION BANK
  1. Let f:RrarrR be defined as f(x) = 10x+7 Find the function g:RrarrR s...

    Text Solution

    |

  2. Let f:WrarrW be defined as f(n) = n-1 if n is odd and f(n) = n+1 i...

    Text Solution

    |

  3. If f:RrarrR is defined by f(x) = x^2-3x+2, find f(f(x))

    Text Solution

    |

  4. Show that the function f:R rarr R given by f(x)=x^3 is injective.

    Text Solution

    |

  5. Given a non empty set X, consider P(X) which is the set of all subsets...

    Text Solution

    |

  6. Find the number of all onto functions from the set {1,2,3 …... n}to i...

    Text Solution

    |

  7. Let S={a, b, c} and T={1,2,3}, Find F^-1 of the following functions F ...

    Text Solution

    |

  8. Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions define...

    Text Solution

    |

  9. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)20 ...

    Text Solution

    |

  10. Show that the relation R on the set N xx N defined by (a, b)R(c, d)...

    Text Solution

    |

  11. If f: R rarr R be a function defined by f(x)=4 x^3-7, show that the fu...

    Text Solution

    |

  12. Consider the binary operation ast : QtoQ where Q is the set of rationa...

    Text Solution

    |

  13. Prove that the function f: Q rarr Q given by f(x)=2 x-3 for all x in Q...

    Text Solution

    |

  14. Prove that the function f: N rarr N , defined by f(x)=x^2+x+1 is one-...

    Text Solution

    |

  15. Let f: R rarr R be a function defined by f(x)=x^2-3 x+2 Find f^' (2) a...

    Text Solution

    |

  16. If f : R rarrR be defined by f(x) = 5x - 3, then prove that f is one-o...

    Text Solution

    |

  17. Let f, g: R rarr R be defined by f(x)=x^2+1and g(x)=sin x. Find f o g ...

    Text Solution

    |

  18. If f, g: R rarr R are defined by f(x)=x^2+3 x+1, g(x)=2 x-3, find (i) ...

    Text Solution

    |

  19. Let * be a binary operation on N, the set of all natural numbers defin...

    Text Solution

    |

  20. Let A=N xx N and let * be a binary operation on A defined by (a, b)*(...

    Text Solution

    |