Results 1 to 4 of 4

Math Help - is this argument valid?

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    9

    is this argument valid?


    some dogs hate cats
    all dogs have fleas
    frodo has fleas and hates cats
    ----------------------------
    therefore Frodo is a dog


    is it valid ? and why?

    the explanation should be something like "if P then Q "............
    Last edited by ana1808; December 11th 2008 at 02:56 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Greengoblin's Avatar
    Joined
    Feb 2008
    From
    UK
    Posts
    182
    No, because "some dogs hate cats" doesn't exclude other species from the hating of cats, and "all dogs have fleas", doesn't exclude others from having fleas, so while Frodo is likely a dog, it's not certain.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,868
    Thanks
    747
    Hello, ana18081

    It is not valid.
    I have a Venn diagram proof.



    Some dogs hate cats
    All dogs have fleas
    Frodo has fleas and hates cats
    ----------------------------
    Therefore: Frodo is a dog


    Is it valid? Why or why not?

    "All dogs have fleas."

    There is a set of all dogs.
    There is a set of all things that have fleas.
    . . \{\text{dogs}\}\:\subset\: \{\text{have fleas}\}

    The Venn diagram looks like this . . .
    Code:
          * - - - - - - - - - - - - - - - - - *
          | Has fleas                         |
          |       * - - - - - - - - - *       |
          |       |                   |       |
          |       |       Dogs        |       |        
          |       |                   |       |
          |       |                   |       |
          |       * - - - - - - - - - *       |
          |                                   |
          * - - - - - - - - - - - - - - - - - *

    "Some dogs hate cats."

    There is a set of all things that hate cats.

    The set of "Dogs" and the set of "Hate Cats" do intersect.

    The Venn diagram looks like this:
    Code:
          * - - - - - - - - - - - - - - - - - *
          | Has fleas                         |
          |       * - - - - - - - - - *       |
          |       | Dogs              |       |
          |       |       * - - - - - + - - - + - - - *
          |       |       |           |       |       |
          |       |       |     X     |       |       |
          |       * - - - + - - - - - *       |       |
          |               |                   |       |
          * - - - - - - - + - - - - - - - - - *       |
                          |                Hates cats |
                          * - - - - - - - - - - - - - *
    There is at least one creature which is a dog and hates cats.



    "Frodo has fleas and hates cats."

    He could be in the section with the "X"
    . . but he also could be in the shaded region.
    Code:
          * - - - - - - - - - - - - - - - - - *
          | Has fleas                         |
          |       * - - - - - - - - - *       |
          |       | Dogs              |       |
          |       |       * - - - - - + - - - + - - - *
          |       |       |           |///////|       |
          |       |       |     X     |///////|       |
          |       * - - - + - - - - - *///////|       |
          |               |///////////////////|       |
          * - - - - - - - + - - - - - - - - - *       |
                          |                Hates cats |
                          * - - - - - - - - - - - - - *

    Therefore, we can not conclude that Frodo is a dog.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ana1808 View Post

    some dogs hate cats
    all dogs have fleas
    frodo has fleas and hates cats
    ----------------------------
    therefore Frodo is a dog


    is it valid ? and why?

    the explanation should be something like "if P then Q "............
    A single counter example will demonstrate that the argument is invalid, so the possibility of existence of a flea infested cat hating hobbit named frodo will prove the argument invalid.

    CB
    Last edited by CaptainBlack; December 12th 2008 at 11:36 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How do I know if an argument is valid or invalid?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: November 24th 2011, 06:41 PM
  2. Logical Argument, valid or not.
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: May 13th 2011, 02:19 PM
  3. Is this argument valid?
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 4th 2009, 09:22 AM
  4. valid or invalid argument?
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 2nd 2009, 03:54 PM
  5. is this a valid argument?
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: December 2nd 2007, 05:30 PM

Search Tags


/mathhelpforum @mathhelpforum