Results 1 to 4 of 4

Math Help - Negating injection function

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    71

    Negating injection function

    A function f: X to Y is injective if for all x, x' E X f(x) = f(x') implies x = x'

    I attempted it and got:

    There exists x, x' E X f(x) not equal to f(x') implies x not equal to x'


    I'm confident I have got the quantifiers correct, but not the next part???
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1606
    Awards
    1
    The negation of f being injective is \left( {\exists x} \right)\left( {\exists y} \right)\left[ {f(x) = f(y) \wedge \left( {x \ne y} \right)} \right].
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2010
    Posts
    71
    Quote Originally Posted by Plato View Post
    The negation of f being injective is \left( {\exists x} \right)\left( {\exists y} \right)\left[ {f(x) = f(y) \wedge \left( {x \ne y} \right)} \right].
    Oh I see

    Because x implies y negated is Not (x implies y)

    Using the implication rule: x and not y
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,657
    Thanks
    1606
    Awards
    1
    Actually it more general. The negation:
    \neg \left( {\forall x} \right)\left[ {P(x) \Rightarrow Q(x)} \right] \equiv \left( {\exists x} \right)\left[ {P(x) \wedge \neg Q(x)} \right]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Rules for negating?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 28th 2011, 04:09 AM
  2. negating the expression
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 22nd 2010, 06:07 AM
  3. Replies: 3
    Last Post: April 18th 2010, 03:18 PM
  4. Negating implications
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 23rd 2009, 09:32 PM
  5. Negating normal form
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: February 26th 2009, 02:14 AM

Search Tags


/mathhelpforum @mathhelpforum