Results 1 to 3 of 3

Math Help - Negation Logic

  1. #1
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163

    Negation Logic

    Write the negation of the logical expression  (p \rightarrow \neg q) \wedge (p \vee q) . Simplify it to the point where the negation symbol appears only in front of the variables  p and  q , do not leave the negation symbol in front of a parenthetical clause.

    Is the answer  (\neg q \wedge \neg p) \vee (\neg p \wedge \neg q) ?
    Last edited by chiph588@; January 11th 2009 at 02:30 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Aug 2008
    Posts
    33
    Alright, I'll try to walk you though this:

    [(p -> q) ^ (p v q)]

    because of (p^q)=p v q we get

    (p -> q) v (p v q)

    because of (p->q)=p^q we get

    (p ^ q) ^ (p v q)

    because of (p v q)=p^q we get

    (p ^ q) ^ (p ^ q)

    From there we just simplify and get:

    (p ^ q) ^ (p ^ q)



    Hope that helps!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,806
    Thanks
    697
    Hello, chiph588@!

    Write the negation of: . (p \to \sim q) \wedge (p \vee q)
    \sim\bigg[(p\to \sim q) \wedge (p \vee q)\bigg]

    . . = \;\sim\bigg[(\sim p \:\vee \sim q) \vee (p \vee q)\bigg]

    . . = \;\sim(\sim p\: \vee \sim q)\: \vee \sim(p \vee q)

    . . = \;(p \wedge q) \vee (\sim p \:\wedge \sim q)

    . . = \;\bigg[(p \wedge q) \:\vee \sim p\bigg] \wedge \bigg[(p  \wedge q) \vee \sim q\bigg]

    . . = \;\bigg[(p \:\vee \sim p) \wedge (q \:\vee \sim p)\bigg] \wedge \bigg[(p \:\vee \sim q) \wedge (q \:\vee \sim q)\bigg]

    . . = \;\bigg[t \wedge (q \:\vee \sim p)\bigg] \wedge \bigg[(p \:\vee \sim q) \wedge t\bigg]

    . . = \;(q \:\vee \sim p) \wedge (p\: \vee \sim q)

    . . = \;(\sim p \vee q) \wedge (\sim q \vee p)

    . . = \;(p \to q) \wedge (q \to p)

    . . = \;p \Longleftrightarrow q

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Negation
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: October 20th 2010, 12:10 PM
  2. Negation help (2)
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: April 15th 2010, 07:49 AM
  3. Negation help
    Posted in the Discrete Math Forum
    Replies: 14
    Last Post: April 13th 2010, 09:20 AM
  4. The Negation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 22nd 2009, 12:55 PM
  5. statement logic, negation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 29th 2009, 03:16 AM

Search Tags


/mathhelpforum @mathhelpforum