Results 1 to 4 of 4

Math Help - proof by contrapositive help

  1. #1
    Super Member
    Joined
    Sep 2008
    Posts
    619

    proof by contrapositive help

    Let a be an integer. Prove by contraposition that if a2 - 11a + 22 is odd then a is even.
    Fill in the gaps in the following proof.

    Suppose a is odd, so a = 2n + 1 for some integer n.
    Then in terms of n, a2 - 11a + 22 = 2(..........)

    so a2 - 11a + 22 is an(.........)

    Hence, by contraposition, if
    a2 - 11a + 22 is odd then a is even.










    Last edited by Tweety; October 17th 2012 at 01:22 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,561
    Thanks
    785

    Re: proof by contrapositive help

    Can you substitute a = 2n + 1 into a - 11a + 22?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2008
    Posts
    619

    Re: proof by contrapositive help

    thats what I was thinking, but am gona ask my teacher who wrote this, cause I dont understand what to do

    and what is 2 being factored out of ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,561
    Thanks
    785

    Re: proof by contrapositive help

    Quote Originally Posted by Tweety View Post
    and what is 2 being factored out of ?
    2 is being factored out of the result of substitution of 2n + 1 for a in a - 11a + 22. To do the substitution, replace a in a - 11a + 22 with 2n + 1 and perform the simplification.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof by contrapositive
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 14th 2010, 04:45 PM
  2. contrapositive proof
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 5th 2010, 02:07 PM
  3. Simple Contrapositive Proof
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: December 19th 2009, 06:03 AM
  4. Contrapositive proof
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: September 27th 2009, 08:36 AM
  5. Proof by Contrapositive
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 13th 2009, 11:31 PM

Search Tags


/mathhelpforum @mathhelpforum