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Math Help - help with truth tables

  1. #1
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    Red face help with truth tables

    Translate the following argument into symbolic form and determine whether it's logically correct by construcing a truth table.

    If the team wins, then the team remains in the playoffs. If the team stays in the playoffs, then the championship is in reach. Therefore, if the team wins, the championship is within reach.
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  2. #2
    Senior Member OReilly's Avatar
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    Quote Originally Posted by chickenwing View Post
    Translate the following argument into symbolic form and determine whether it's logically correct by construcing a truth table.

    If the team wins, then the team remains in the playoffs. If the team stays in the playoffs, then the championship is in reach. Therefore, if the team wins, the championship is within reach.

    Well, we can transform these sentences into symbols.

    Lets say
    A = "team wins"
    B = "team remains (stays) in the playoffs"
    C = "championship is in reach"


    So, we have A -> B, B -> C and [(A -> B) AND (B -> C)] -> (A -> C).

    So, construct table with columns A,B,C, A -> B, B -> C, A -> C and [(A -> B) AND (B -> C)] -> (A -> C) and put every value true or false for A,B,C and fill A -> B, B -> C, A -> C and [(A -> B) AND (B -> C)] -> (A->C) according to logical rules.
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