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Math Help - Testing validity

  1. #1
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    Testing validity

    Hi, This is my first ever post on this fora so a warm Hello to all

    my question is:
    how will we varify the validity of following argument

    john will become Good-Actor or he will not become a Tv-Star.
    he will become a Tv-Star.
    Therefore he will become a Good-Actor.

    yeah, pretty basic, i know, but i am a bit confused while performing its logical steps (newely joined Discrete Mathematics classes).
    any help will be appriciated.

    respects
    rahat
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  2. #2
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    As for as I understand the solution should be as follows

    a = John will become a good actor
    s = John will becomea tv star

    Premises 1 = john will become Good-Actor or he will not become a Tv-Star.
    = a OR ~s

    Premises 2 = John will become a Tv-Star.
    = s

    Conclusiont = Therefore he will become a Good-Actor.
    = a

    and if we construct a Truth table for it

    a l s l ~s l a OR ~s l a
    ----------------------------------
    T l T l F l T l T
    ----------------------------------
    T l F l T l T l T
    ----------------------------------
    F l T l F l F l F
    ----------------------------------
    F l F l T l T l F
    ----------------------------------

    So the argument is valid
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  3. #3
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    ( (a \/ ~s) /\ s ) -> a is a tautology (a->a is always true), so it is a valid argument.
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  4. #4
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    Quote Originally Posted by vagabond View Post
    ( (a \/ ~s) /\ s ) -> a is a tautology (a->a is always true), so it is a valid argument.
    Thanks for the reply vagabond...
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