Results 1 to 6 of 6

Math Help - logical implication

  1. #1
    Banned
    Joined
    Jul 2009
    Posts
    107

    logical implication

    Does X\subseteq Y logically imply xεX and xεY ??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: logical implication

    Quote Originally Posted by alexandros View Post
    Does X\subseteq Y logically imply xεX and xεY ??
    Absolutely not!
    It means \text{If }x\in X\text{ then }x\in Y.
    Or equivalently x\notin X\text{ or }x\in Y.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,527
    Thanks
    773

    Re: logical implication

    I would even start by saying that x has not been defined...
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Jul 2009
    Posts
    107

    Re: logical implication

    Yes i agree with both of you,but how do you show that to somebody who insists otherwise??
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1

    Re: logical implication

    Quote Originally Posted by alexandros View Post
    Yes i agree with both of you,but how do you show that to somebody who insists otherwise??
    In this matter I absolutely agree with emakarov's reply.
    \left( {X \subseteq Y} \right) \Leftrightarrow \left( {\forall x} \right)\left[ {x \in X \to x \in Y} \right].

    Ask your protagonists does imply that \left( {\forall x} \right)\left[ {x \in X \wedge x \in Y} \right]
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    Jul 2009
    Posts
    107

    Re: logical implication

    O.k Thanks we carry on tomorrow
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logical Implication
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2010, 01:33 AM
  2. Prove/disprove using logical using logical arguments
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 24th 2010, 06:29 AM
  3. Replies: 3
    Last Post: January 21st 2010, 07:45 AM
  4. Logical Implication
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 12th 2008, 05:48 AM
  5. Replies: 5
    Last Post: August 19th 2008, 06:24 PM

Search Tags


/mathhelpforum @mathhelpforum