Home
Class 12
MATHS
Find the number of all onto functions f...

Find the number of all onto functions from the set `{1, 2, 3, , n)`to itself.

Text Solution

Verified by Experts

The number of all onto functions from the set { 1, 2, 3, ... , n} to itself will be equal to number of permutations of 1, 2, 3 , .. , n i.e.,`""^(n)P_n = lfloor n.`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercise 1.4|13 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Find the number of all onto functions from the set A={1,2,3, ,n} to itself.

Write the number of all one-one functions from the set A{a,b,c} to itself.

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

Let S be the set of all function from the set {1, 2, …, 10} to itself. One function is selected from S, the probability that the selected function is one-one onto is :

If P(S) denotes the set of all subsets of a given set S, then the number of one-to-one functions from the set S={1,2,3} to the set P(S) is

The total number of onto functions from the set {1,2,3,4) to the set (3,4,7) is

Find the number of onto function between two sets A=(1,2,3,4) and B=(4,5)

The total number of onto functions from the set A={a,b,c,d,e,f} to the set B={1,2,3} is lambda then (lambda)/(100) is

NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
  1. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  2. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  3. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

    Text Solution

    |

  4. Show that the function f: R rarr { x in R: -1 lt x lt 1 } defined by ...

    Text Solution

    |

  5. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  6. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  7. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  8. Given a non-empty set X, consider P(X) which is the set of all subs...

    Text Solution

    |

  9. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  10. Find the number of all onto functions from the set {1, 2, 3, , n)to ...

    Text Solution

    |

  11. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  12. Consider the binary operations*: RxxR->R and o: RxxR->R defined as ...

    Text Solution

    |

  13. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  14. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

    Text Solution

    |

  15. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  16. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  17. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  18. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

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

    Text Solution

    |