Results 1 to 7 of 7

Math Help - True or false: If someone in the library is wearing a hat, then I can steal it.

  1. #1
    Newbie
    Joined
    Oct 2011
    Posts
    20

    True or false: If someone in the library is wearing a hat, then I can steal it.

    Assuming I am in the library and I am capable of stealing hats.

    p: someone in the library is wearing a hat
    q: I can steal it
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie mintsmike's Avatar
    Joined
    Mar 2009
    Posts
    5

    Re: True or false: If someone in the library is wearing a hat, then I can steal it.

    Are you looking for a logical implication. Like P \Rightarrow Q? In which case that would be right. P does imply Q.

    However the converse, that Q implies P, is also true and so it is a logical equivalence
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,393
    Thanks
    1327

    Re: True or false: If someone in the library is wearing a hat, then I can steal it.

    But does "am capable of stealing hats" mean "can steal any hat"?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member MacstersUndead's Avatar
    Joined
    Jan 2009
    Posts
    291
    Thanks
    32

    Re: True or false: If someone in the library is wearing a hat, then I can steal it.

    For statement Q: "I can steal it" , 'it' doesn't necessarily have to refer to a hat. 'it' could be a book in the library, for example
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,314
    Thanks
    695

    Re: True or false: If someone in the library is wearing a hat, then I can steal it.

    if you are capable of stealing any hat from anyone in the library, and you cannot steal a hat from someone in the library (that is, you are not capable of stealing their hat), it must be that they are not wearing one, eh?

    (contrapositive is true, thus the implication is true).

    the real trouble here is that "natural languange" (such as English) doesn't "fit exactly" to "logical language". statements in English, for example, can be ambiguous (they're "maybe-true/maybe-false"), whereas statements within logic must be one OR the other (and certainly not BOTH)!

    so trying to "illustrate" logical reasoning with examples in "everyday language" is a path fraught with peril and pit-falls. one must choose their words VERY carefully, and the clever ones among us will rush to point out the loop-holes.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,034
    Thanks
    49

    Re: True or false: If someone in the library is wearing a hat, then I can steal it.

    Just bumping this over the spam
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Dec 2009
    Posts
    68
    Thanks
    1

    Re: True or false: If someone in the library is wearing a hat, then I can steal it.

    Any statement can never be proven true beyond a shadow of a doubt by examples that follow the rule of inference. However, it only takes one counterexample to prove a statement false.

    For example: Suppose you want to know the truth value of 'If A then B'. In general for any math or nonmath statements A, you can find as many examples of 'A' and each time and conclude 'B' but you can never be entirely sure that you can conclude B. In your if-then statement, as long as you can show that you *can* steal the hat if a person in the library wears it, your if-then statement is true. Otherwise, if you can't show that you can steal the hat, your argument is weak. Also, if someone in the library is wearing a hat and you can't steal it, your statement would be false (For a given statement If P then Q, if it is known that P results in not Q, then 'P but not Q' is an example of a counterexample).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 19th 2012, 04:20 PM
  2. Replies: 7
    Last Post: October 5th 2011, 12:45 PM
  3. Replies: 1
    Last Post: October 4th 2011, 02:19 AM
  4. how come false AND false is true?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 24th 2010, 07:41 AM
  5. True or False. Prove if true show counter example if false.
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 2nd 2010, 10:54 AM

Search Tags


/mathhelpforum @mathhelpforum