1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

~(p->q) of part of A Probabilistic Proof of Wallis's Formula for pi

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Write in symbols the negation of the theorem stated in part a.

    part a:We immediately see that if g(x) is a nonnegative continuous function whose integral is finite, then there exists an a>0 such that a*g(x) is a continuous probability distribution (take a=1/[tex]\int g(x)dx[/tex] from -[tex]\infty[/tex] to [tex]\infty[/tex]).

    The negation of P implies Q is equivalent to not P or Q.

    The issue is with the P part.

    Is ~P= g(x) isn't a nonnegative continuous fuction whose integral isn't finite?

    I am not sure if both is parts need to be negated or just one.

    Then for the Q part it is just itself starting with the existential quantifier.
  2. jcsd
  3. Feb 13, 2010 #2
    ~(P => Q) is equivalent to "P and not Q."

    Since you don't need the negation of P, does that solve your problem?
    Last edited: Feb 13, 2010
  4. Feb 13, 2010 #3
    Just for completeness sake:

    I suppose P is the statement "g(x) is a non-negative continuous function whose integral is finite." I would re-write this as "g(x) is a function which is non-negative and continuous and whose integral is finite" to emphasize the internal logical structure. Since ~(a and b and c) = ~a or ~b or ~c, the negation of P is:

    "g(x) is a function which is not continuous or assumes negative values or whose integral diverges."
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - part Probabilistic Proof Date
Lim sup proof Mar 12, 2018
Integration by parts/substitution Nov 2, 2017
Solving an Integral Sep 23, 2017
Open and Closed Sets - Sohrab Exercise 2.4.4 - Part 3 ... Aug 13, 2017