Home
Class 12
MATHS
Prove that f:X to Y is injective iff for...

Prove that `f:X to Y` is injective iff for all subsets A, B of `X, f (A cap B) =f(A) cap f(B)`.

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2020

    SHARAM PUBLICATION|Exercise EXERCISE|47 Videos

  • THREE DIMENSIONAL GEOMETRY

    SHARAM PUBLICATION|Exercise EXAMPLE|96 Videos

Similar Questions

Explore conceptually related problems

Prove that f:X rarr Y is injective iff for all subsets A,B of X,f(A nn B ) = f(A) nn f(B) .

Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B)) =B.

Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A sube X .

Prove that f: X rarr Y is surjective iff for all A sube X,(f(A))' sube f(A') , where A' denotes the complement of A in X.

Prove that f(x)=|x| is not differetiable at x=0

Let f be defined by f (x)=2x + 1 for all xinR . Show that f is bijective and determine the inverse of f. Find f^(-1)(0),f^(-1)(2) and f^(-1)(-1) .

If f:X to Y is a function. Define a relation R on X given by R={(a, b): f(a)=f(b)}. Show that R is an equivalence relation on X.

Prove that for any f:X rarr Y , f o id_x = f =id_Y of.

Show that the functions are injective f(x) = sinx on [ 0, (pi)/(2)]

SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
  1. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

    Text Solution

    |

  2. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

    Text Solution

    |

  3. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

    Text Solution

    |

  4. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

    Text Solution

    |

  5. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

    Text Solution

    |

  6. Prove that for any f:X rarr Y , f o idx = f =idY of.

    Text Solution

    |

  7. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

    Text Solution

    |

  8. Let f:XrarrY. If there exists a map g:YrarrX such that g of=idxand fo ...

    Text Solution

    |

  9. If ff(x)=cos[pi^2]x+cos[-pi^2]x where [x] stands for the greatest inte...

    Text Solution

    |

  10. If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...

    Text Solution

    |

  11. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

    Text Solution

    |

  12. Prove that the relation R on the set Z of all integers defined by R={(...

    Text Solution

    |

  13. Let n be positive integer and a function f be defined as f(n)={(0 , wh...

    Text Solution

    |

  14. If f:RrarrR defined by f(x)=5x-8 for all x inR, then show that f is in...

    Text Solution

    |

  15. Show that the inverse of a bijective function is unique.

    Text Solution

    |

  16. Show that the inverse of a bijective is also a bijection.

    Text Solution

    |

  17. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

    Text Solution

    |

  18. Prove that the greatest integer function f:R rarr R, given by f(x) = [...

    Text Solution

    |

  19. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

    Text Solution

    |

  20. Show that the fuction f:RrarrR defined by f (x)=sin x is neither one-...

    Text Solution

    |