Home
Class 12
MATHS
Find the number of all one-one functions...

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

Text Solution

Verified by Experts

Since f is one-one, thus every element of `{1,2,3}` has either of image `{1,2,3}` an that image is unique.
Total no. of one-one functions = `3! = 3×2×1=6`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.4|13 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.2|12 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 1.3|14 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 13.2|18 Videos

  • SETS

    NCERT|Exercise EXERCISE 1.3|1 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.

Write total number of one-one functions from set A={1,\ 2,\ 3,\ 4} to set B={a ,\ b ,\ c} .

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

Let A={a, b, c} and B={-2, -1, 0 ,1 ,2} .Write the total number of one-to-one functions from set A to set B .

Statement -2 : The number of functions from A = {1, 2, 3} to B = {2008, 2009} is 8. and Statement-2 : The number of all possible functions from A = {1, 2, 3} to B = {2008, 2009} is 9.

6. The number of many one functions from A = {1, 2, 3} to B = {a,b,c,d) is 1) 64 2) 24 3)40 4

If A= {1,3,5,7} and B= {1,2,3,4,5,6,7,8} , then the number of one-to-one functions from A into B is

NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Let f : N ->R be a function defined as f(x)=4x^2+12 x+15. Show that f...

    Text Solution

    |

  2. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

    Text Solution

    |

  3. Consider f : {1, 2, 3} ->{a , b , c}and g : {a , b , c} ->{a p p l e ,...

    Text Solution

    |

  4. Consider functions f and g such that composite gof is defined and is ...

    Text Solution

    |

  5. Are f and g both necessarily onto, if gofis onto?

    Text Solution

    |

  6. Let f : {1, 2, 3}->{a , b , c}be one-one and onto function given by f...

    Text Solution

    |

  7. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , where...

    Text Solution

    |

  8. Let S = {1, 2, 3}. Determine whether the functions f : S->S defi...

    Text Solution

    |

  9. Show that addition, subtraction and multiplication are binary operati...

    Text Solution

    |

  10. Consider the identity function IN : N->N defined as, IN(x)=x for al...

    Text Solution

    |

  11. Let R be a relation on the set A of ordered pairs of positive integer...

    Text Solution

    |

  12. Let X={1,2,3,4,5,6,7,8,9}. Let R be a relation in X given by R1={(x,y)...

    Text Solution

    |

  13. Show that -ais not the inverse of a in Nfor the addition operation +...

    Text Solution

    |

  14. If R1 and R2 are equivalence relations in a set A, show that R1nnR2 i...

    Text Solution

    |

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

    Text Solution

    |

  16. Let A={1,\ 2,\ 3} . Then, show that the number of relations containi...

    Text Solution

    |

  17. Let f : X->Ybe a function. Define a relation R in X given by R = {(a ...

    Text Solution

    |

  18. Determine which of the following binary operations on the set N are a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |