Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Plato

Thread: Proving implication

  1. #1
    Senior Member
    Joined
    Mar 2017
    From
    Massachusetts
    Posts
    346
    Thanks
    3

    Question Proving implication

    Hi,

    I'm hoping someone can help me with proving the following statement: $\forall x \in\mathbb{R}, P(x) \Rightarrow \forall y \in\mathbb{R}, P(y)$.

    First, I assume $\forall x \in\mathbb{R}, P(x)$.
    Then I say "Let $y\in\mathbb{R}.$"
    ..... how do I finish this proof?

    It is clear to me that this statement is true. I can't say P(y) is true because x = y, since x is not a defined value. I would really appreciate help!!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,398
    Thanks
    3286
    Awards
    1

    Re: Proving implication

    Quote Originally Posted by otownsend View Post
    help me with proving the following statement: $\forall x \in\mathbb{R}, P(x) \Rightarrow \forall y \in\mathbb{R}, P(y)$.
    It is clear to me that this statement is true. I can't say P(y) is true because x = y, since x is not a defined value. I would really appreciate help!!!!
    To do this I need to use conditional proof, C.P.
    $\forall x \in\mathbb{R}, P(x) \Rightarrow \forall y \in\mathbb{R}, P(y)$.
    $\forall x \in\mathbb{R}, P(x)$. assunption.
    $P(z)$ UI (universal instantiation)
    $(\forall y)[P(y)]$ UG (universal generalization).
    $(\forall x) [P(x)] \Rightarrow (\forall y)[ P(y)]$ CP (conditional proof).

    Now I am with you in that this is a very strange looking proof.
    However, almost the exact proof is found in the textbook SYMBOLIC LOGIC by Copi.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Implication in logic
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: Sep 14th 2013, 08:06 AM
  2. logical implication
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: Jun 13th 2011, 04:09 PM
  3. Logical Implication
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2010, 01:33 AM
  4. Logical Implication
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Sep 12th 2008, 05:48 AM
  5. Replies: 5
    Last Post: Aug 19th 2008, 06:24 PM

Search Tags


/mathhelpforum @mathhelpforum