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Math Help - If p then Q truth table

  1. #1
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    If p then Q truth table

    p q p-->q
    T T T
    T F F
    F T T
    F F T

    Why do the last two columns in the truth table equal True? This really does not make any sense to me.
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  2. #2
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    Re: If p then Q truth table

    Quote Originally Posted by IDontunderstand View Post
    p q p-->q
    T T T
    T F F
    F T T
    F F T


    Why do the last two columns in the truth table equal True? This really does not make any sense to me.
    I think that you mean rows.
    A false statement implies any statement.
    If false then anything is true.
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  3. #3
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    Re: If p then Q truth table

    I did mean rows.
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  4. #4
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    Re: If p then Q truth table

    Hello, IDontunderstand!

    Plato is absolutely correct . . .

    I too was puzzled when I first learned about Implication.
    This is how my professor explained it.


    Consider this scenario.

    Your professor makes you this promise:
    . . If you get 100% on the final exam, then you will get an "A" for the course.
    (Imagine further than you don't trust him, so you get this in writing,
    . . signed and notarized before witnesses!)

    Under what circumstances has he broken his promise,
    . . (and you can start a class-action suit)?


    Consider the four possible outcomes:

    (1) You got 100% on the Final and you got an "A" for the course.
    . . .He kept his promise . . . no problem!

    (2) You got 100% on the Final and you did not get an "A".
    . . .He broke his promise . . . call your lawyer!

    (3) You did not get 100% and you got an "A".
    . . .Maybe you got "only" 99% and your average is still "A".
    . . .No basis for a lawsuit.

    (4) You did not get 100% and you did not get an "A".
    . . .Maybe you got only 60% and your average dropped to a "B".
    . . .Again, no basis for a lawsuit.


    In brief: his promise involves only what would happen if you got 100% on the final.
    No promises were made about what would happen if you did not get 100%.

    And that is why . \begin{Bmatrix} T \to T \\ F \to T \\ F \to F\end{Bmatrix} are all True.

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