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Math Help - Truth tables Propositional Logic.

  1. #1
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    Truth tables Propositional Logic.

    i.) Truth table for these:

    Force always caused acceleration.

    my guess: Force -> acceleration

    F A F->A
    T T T
    T F F
    F T F
    F F F
    /////////////////////////////////

    You win in tennis if and only if you win more sets than your opponent.

    my guess: win=>more sets than opponent

    win / more sets / win=>more sets than opponent
    T T T
    T F F
    F T F
    F F F

    /////////////////////////////////

    You are allowed to drink only if you are aged above 21.

    myguess: 21->you can drink.

    not sure if I should do a truth table using 21->you can drink or 21^can drink
    ?
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  2. #2
    MHF Contributor
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    Force always caused acceleration.

    my guess: Force -> acceleration

    F A F->A
    T T T
    T F F
    F T F
    F F F
    Implication is false in one case only: when the premise is true and the conclusion is false. What you have is a truth table for conjunction.

    You win in tennis if and only if you win more sets than your opponent.

    my guess: win=>more sets than opponent

    win / more sets / win=>more sets than opponent
    T T T
    T F F
    F T F
    F F F
    Since the English sentence has "if and only if", this statement is a biconditional. It is often denoted by W <-> M or W <=> M, and is equivalent to (W -> M) /\ (M -> W). It is true precisely when W and M have the same truth values, so, it is true in two of the four rows.

    You are allowed to drink only if you are aged above 21.

    myguess: 21->you can drink.
    It would have been "21->you can drink" if the sentence had said just "if" instead of "only if". The rule is: what follows a simple "if" is the premise. For example, both "If A, then B" and "B if A" mean A -> B. "Only if" makes implication go in the opposite direction to "if". So, "A only if B" means A -> B.

    using propositional logic unification and resolution.
    Resolution and unification are syntactic methods of manipulating formulas. They view formulas as strings of symbols. They are very different from truth tables, which assign truth values (semantics, or meaning) to formulas.
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