Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Negation for proposition

  1. Jan 17, 2016 #1
    5tymp2.jpg

    my attempt.

    Let P = At least one a and at least one b
    Let Q = r=a/b


    Hence the proposition is simplified to,

    For all r where P Then Q

    Negation:
    Not all
    r where P Then Q
    = Atleast one R When Not(P Then Q)

    Not(P Then Q) = P And Not Q

    Hence
    Atleast one R When Not(P Then Q)
    = Atleast one R When P And Not Q

    After this step i substitute back P and Q.
    Is this way correct?
     
  2. jcsd
  3. Jan 17, 2016 #2

    WWGD

    User Avatar
    Science Advisor
    Gold Member

    There is a general method for negating that goes from the outermost (left-most) statement : For all is negated into there is
    There is a general method for negating compound statements : the negation is done from the leftmost to rightmost statement: first you negate the "for all" into there exists
    and then you negate the A and B statement into NotA or NotB , where A is There exists an integer Z , negated into " For all a in Z "and so on. Informally, the negation says that there exists a Rational that is not the ratio of two integers.
     
  4. Jan 17, 2016 #3
    Hi so the ans is.

    There exists a rational number r, Where all integer a and all integer b such that r != a/b

    May i know what is "such that' converted to? For my case i tot it means "then"
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Negation for proposition
  1. Proposition Negation (Replies: 6)

  2. Propositional Logic (Replies: 3)

Loading...