Results 1 to 4 of 4

Math Help - ab is odd

  1. #1
    Senior Member
    Joined
    Apr 2008
    From
    Vermont
    Posts
    318

    ab is odd

    If ab is odd, then a and b are both odd. I'm not quite sure how to go about proving this. I think I need to assume ab is odd or maybe do a proof by contradicition?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by kathrynmath View Post
    If ab is odd, then a and b are both odd. I'm not quite sure how to go about proving this. I think I need to assume ab is odd or maybe do a proof by contradicition?
    Just consider all the cases:

    a and b odd,
    a even b odd,
    a odd b even,
    a even b even.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Apr 2008
    From
    Vermont
    Posts
    318
    Quote Originally Posted by CaptainBlack View Post
    Just consider all the cases:

    a and b odd,
    a even b odd,
    a odd b even,
    a even b even.

    CB
    But would that be an acceptable proof? I'm trying to do a formal proof.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by kathrynmath View Post
    But would that be an acceptable proof? I'm trying to do a formal proof.
    The Captain gave the most straight forward and perfectly acceptable approach to the problem. as an alternative, you may want to use the contrapositive, then you only have to check 3 cases

    Assume a and b are not both odd, then you have 3 cases:

    (1) a is even but b is odd
    (2) a is odd but b is even
    (3) a and b are both even

    in all cases, we have ab even, so the proof by contrapositive follows
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum