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Someone please help me

  1. Feb 2, 2009 #1
    1. I am a 47 year old man returning to school after so many years. I really need helpwith my Math. I am working on another degree and I have forgot everything in math.

    Here is the problem

    Let p be “The object belongs to set A.” Let q be
    “the object belongs to set B.”
    All A is B is equivalent to p →q.
    No A is B is equivalent to p →∼q.
    Some A is B is equivalent to p ∧ q.
    Some A is not B is equivalent to p ∧∼q



    Please help!

    Paul Murphy



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 2, 2009 #2
    Truth tables are related to Euler circles. Arguments in
    the form of Euler circles can be translated into statements
    using the basic connectives and the negation as follows:
    Let p be “The object belongs to set A.” Let q be
    “the object belongs to set B.”
    All A is B is equivalent to p →q.
    No A is B is equivalent to p →∼q.
    Some A is B is equivalent to p ∧ q.
    Some A is not B is equivalent to p ∧∼q.
    Determine the validity of the next arguments by
    using Euler circles, then translate the statements into
    logical statements using the basic connectives, and
    using truth tables, determine the validity of the
    arguments. Compare your answers.
    (a) No A is B. (b) All B is A.
    Some C is A. All C is A.
    ∴ Some C is not B. ∴ All C is
     
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