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Math Help - How would I do this truth table?

  1. #1
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    How would I do this truth table?

    How would I draw out the truth table for something with 3 things? (p, q and r). I am only used to doing 2 things (p and q) Here are the two things that I am supposed to check whether or not they are logically equivalent.

    P = (p --> q) ^ (q --> r), Q = p --> r

    All I need to know is how to set up the truth table, I can do the calculations myself.
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  2. #2
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    Re: How would I do this truth table?

    Quote Originally Posted by kmjt View Post
    How would I draw out the truth table for something with 3 things? (p, q and r). I am only used to doing 2 things (p and q) Here are the two things that I am supposed to check whether or not they are logically equivalent.
    P = (p --> q) ^ (q --> r), Q = p --> r
    All I need to know is how to set up the truth table, I can do the calculations myself.
    Have a look at this.
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  3. #3
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    Re: How would I do this truth table?

    Hello, kmjt!

    How would I draw out the truth table for something with 3 things?

    . . \big[(p \to q) \wedge (q \to r)\big] \;\to\; (p \to  r)

    . . \begin{array}{|c|c|c||c|} p&q&r& \big[(p \to q) \wedge (q\to r)\big] \:\to\:(p \to r) \\ \hline T&T&T& \\ T&T&F& \\ T&F&T& \\ T&F&F& \\ F&T&T& \\ F&T&F& \\ F&F&T& \\ F&F&F& \\ \hline \end{array}

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  4. #4
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    Re: How would I do this truth table?

    As another hint: p -> q == ~p v q
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  5. #5
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    Re: How would I do this truth table?

    Quote Originally Posted by CaramelCardinal View Post
    As another hint: p -> q == ~p v q
    What does "==" mean?
    If it means "if and only if" then please learn to use LaTeX notation.
    For example [TEX]\left( {p \Rightarrow q} \right) \Leftrightarrow \left( {\neg p \vee q} \right)[/TEX] gives \left( {p \Rightarrow q} \right) \Leftrightarrow \left( {\neg p \vee q} \right).

    Do you see why that is so much easier to read?
    Why that is so much more professional?
    Why that is then so much more helpful?
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  6. #6
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    Re: How would I do this truth table?

    I already figured this out, thanks again Plato!
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