Results 1 to 6 of 6

Thread: Simple Contrapositive Proof

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    64

    Simple Contrapositive Proof

    Let $\displaystyle n \in \mathbb{Z}$ be an integer with $\displaystyle n \ge 0$. State and prove the contrapositive of the
    following statement: If $\displaystyle n^2$ is an odd number, then n is odd.

    I can prove this by substituting n for 2m and proving $\displaystyle n^2$ is even. but am unsure if this is the final extent to what i need to proof, how far do i need to go to prove this, should i give more examples?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by Stylis10 View Post
    Let $\displaystyle n \in \mathbb{Z}$ be an integer with $\displaystyle n \ge 0$. State and prove the contrapositive of the
    following statement: If $\displaystyle n^2$ is an odd number, then n is odd.

    I can prove this by substituting n for 2m and proving $\displaystyle n^2$ is even. but am unsure if this is the final extent to what i need to proof, how far do i need to go to prove this, should i give more examples?
    The contrapositive is that if $\displaystyle n^2$ is not odd (even) then $\displaystyle n$ is not odd (even). Prove that (try contradiction).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2008
    Posts
    64
    Quote Originally Posted by Drexel28 View Post
    The contrapositive is that if $\displaystyle n^2$ is not odd (even) then $\displaystyle n$ is not odd (even). Prove that (try contradiction).
    But then am i not just going back and provign the original statement and therfore not actually proving it through contrapositive?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by Stylis10 View Post
    But then am i not just going back and provign the original statement and therfore not actually proving it through contrapositive?
    No. It is quite different.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2008
    Posts
    64
    ok, i think i understand, i have come up with this:

    $\displaystyle n$ must be even for $\displaystyle n^2$ to be even,
    let $\displaystyle n = 2m+1$
    $\displaystyle (2m+1)^2 = 4m^2+4m+1$
    $\displaystyle = 2Q + 1$ which is odd, therefore $\displaystyle n$ must be even for $\displaystyle n^2$ to be even and hence $\displaystyle n$ must be odd for $\displaystyle n^2$ to be odd.

    or have i just done my own thing here and gone off on a tangent?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by Drexel28 View Post
    The contrapositive is that if $\displaystyle n^2$ is not odd (even) then $\displaystyle n$ is not odd (even). Prove that (try contradiction).
    I dont think that is right. Read this.

    The contrapositive of "If $\displaystyle n^2$ is an odd number, then $\displaystyle n$ is odd" is "If $\displaystyle n$ is even then $\displaystyle n^2 $ is even".

    So Stylis10, you were right in your first post when you explained the proof in the last line.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with a proof - Contrapositive or Contradiction?
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: Sep 24th 2010, 08:41 AM
  2. Proof by contrapositive
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Sep 14th 2010, 03:45 PM
  3. contrapositive proof
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 5th 2010, 01:07 PM
  4. Contrapositive proof
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: Sep 27th 2009, 07:36 AM
  5. Proof by Contrapositive
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 13th 2009, 10:31 PM

Search Tags


/mathhelpforum @mathhelpforum