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Math Help - Truth Tables

  1. #1
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    Truth Tables

    Hi,

    I'm currently going through past exams papers as part of my revision for my upcoming exams, however the past papers that I am using do not include answers, so I'm not sure if I'm on the right track or not.

    The question I'm working on is:

    Which of the following columns (A) to (D) correctly completes the truth table for the expression?

    The expression is 'p implies not q and r'. (I'm not sure how to type it mathematically).


    p q r (A) (B) (C) (D)
    F F F T T F T
    F F T F T T T
    F T F T T F T
    F T T F T T T
    T F F F F F F
    T F T F T T F
    T T F T F F T
    T T T F F T F


    I have tried to work it out and I've come out with column C. Can anybody tell me if that's correct, or where I might of gone wrong if it's not?
    Last edited by Gall1987; May 4th 2011 at 07:22 AM.
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  2. #2
    A Plied Mathematician
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    A couple of comments.

    1. What is your expression?
    2. You can use WolframAlpha to generate truth tables thus.
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  3. #3
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    Hello, Gall1987!

    Which of the following columns (A) to (D)
    correctly completes the truth table for the expression?

    \begin{array}{ccc|cccc} p & q & r & (A) & (B) & (C) & (D) \\ \hline \\[-4mm] F & F & F & T & T & F & T \\ F & F & T & F & T & T & T \\ F & T & F & T & T & F & T \\ F & T & T & F & T & T & T \\ T & F & F & F & F & F & F \\ T & F & T & F & T & T & F \\ T & T & F & T & F & F & T \\ T & T & T & F & F & T & F \end{array}

    What is "the expression"?

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  4. #4
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    Quote Originally Posted by Ackbeet View Post
    A couple of comments.

    1. What is your expression?
    2. You can use WolframAlpha to generate truth tables thus.
    Oh excellent, that looks like a good website to use. I have tried to use it to calculate the above equation though and it is displaying as this.

    I can't get the equation to display correctly to calculate the truth table.
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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, Gall1987!


    What is "the expression"?

    The expression is P implies not q and r. Sorry, I thought I'd included it, but I'm not sure how to type it mathematically on here.
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  6. #6
    A Plied Mathematician
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    Quote Originally Posted by Gall1987 View Post
    Oh excellent, that looks like a good website to use. I have tried to use it to calculate the above equation though and it is displaying as this.

    I can't get the equation to display correctly to calculate the truth table.
    Yeah, that's weird. I tried a number of things that didn't work. I'm going to try the equivalent expression:

    p \to r if and only if

    \neg p \lor r.

    The result is here.

    Update: Curiouser and curiouser! It worked this time, although there are no reassuring parentheses. The truth table is the correct one for your expression.
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