Home
Class 12
MATHS
Let f : X rarr Y be an function. Define ...

Let `f : X rarr Y` be an function. Define a relation R in X given by : R = {(a,b) : f(a) = f(b)}`. Examine, if R is an equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTION

    MODERN PUBLICATION|Exercise EXAMPLE|212 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|543 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos

Similar Questions

Explore conceptually related problems

Let f : X rarr Y be a function. Define a relation R in X given by R = {(a, b): f (a) = f (b)} Examine whether R is an equivalence relation or not.

Show that the relation R in the set : R = {x : x in Z, 0 le x le 1 2}, given by : R = {(a, b): a = b} are equivalence relations.

Let f : R rarr R be the functions defined by f(X) = x^3 + 5 , then f^-1 (x) is

Let f: R rarr R be defined as f(X) = 3x. Then

Prove that the relation R in Z of integers given by: R = {(x, y): 3x - 3y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (6- 5x)/7 is an invertible function, find f^-1 .

Prove that the relation R in Z of integers given by: R = {(x, y): x - y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (3- 2x)/4 is an invertible function, find f^-1 .

Prove that the relation R in Z of integers given by: R = {(x, y): 2x - 2y is an integer } is an equivalence relation. [3] If f: RrarrR defined by f(x) = (4- 3x)/5 is an invertible function, find f^-1 .

Let Z be the set of all integers and R be the relation on Z defined as R = (a,b) : a,b in Z and a-b is divisible by 5) Prove that R is an equivalence relation.

A function f : R rarr R is defined by f(x) = 4x^3 +5, x in R examine if f is one-one and onto.

Let f : R rarr R be defined by f(x) = 1/x AA x inR , then f is

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Let '*' be the binary operation defined on R by a*b = 1 + ab AA a,binR...

    Text Solution

    |

  2. Is the binary operation'*' defined on Z (set of integers) by m*n = m-n...

    Text Solution

    |

  3. Let f : X rarr Y be an function. Define a relation R in X given by : R...

    Text Solution

    |

  4. If R1 and R2 are equivalence relations in a set A, show that R1 nn R...

    Text Solution

    |

  5. Show that the number of equivalence relation in the set {1, 2, 3} cont...

    Text Solution

    |

  6. Show that the number of equivalence relation in the set {1, 2, 3} cont...

    Text Solution

    |

  7. Let A = {1,2,3}. Then show that the nmber of relations (1,2) and (2,3)...

    Text Solution

    |

  8. Find the number of all one-one functions from set A = {1, 2, 3} to its...

    Text Solution

    |

  9. Find the number of all onto functions formthe set {1,2,3,….,n} to itse...

    Text Solution

    |

  10. Give examples of two one-one function f1 and f2 from R to R such that ...

    Text Solution

    |

  11. Show that if f1 and f2 are one-one maps from r to R, then the product....

    Text Solution

    |

  12. Lert f : X rarr Y be such that fof = f. Show that f is onto if and onl...

    Text Solution

    |

  13. Consider the identity function IN : N rarr N defined as IN (x) = x, fo...

    Text Solution

    |

  14. Find fof^-1 and f^-1 of for the function: f(x) = 1/x, x ne0, also prov...

    Text Solution

    |

  15. Show that the number of binary operations on {1, 2} having 1 as identi...

    Text Solution

    |

  16. Determine whether the following binary operation on the set N is assoc...

    Text Solution

    |

  17. Determine , whether the following binary operation on the set N is ass...

    Text Solution

    |

  18. Consider the binary operation: R xx R rarr R defined as : a** b = |...

    Text Solution

    |

  19. Define a binary operation * on the set A = {0,1,2,3,4,5}, given by a *...

    Text Solution

    |

  20. Given set A = {1,2,3}, then the relation : R = {(1,1),(2,2),(3,3)} is ...

    Text Solution

    |