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Math Help - Truth Table

  1. #1
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    Truth Table

    How do I construct the truth table for the following proposition: Yfrog Image : yfrog.com/59truthtablep

    TY in advance.

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  2. #2
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    The same way you construct any truth table: one piece at a time. You only have two variables, which means you'll only need 4 rows. How did you start out?
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  3. #3
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    Okay so the first two columns consist of all combinations of p and q, ie TT, TF, FT and FF. Then does the next column have the heading q^p?
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  4. #4
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    Looks like a good first step. What values do you get?
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  5. #5
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    To be honest I'm not sure how to figure the values out. This is what's confusing me. Here's a guess: T, F, F, T or maybe they're all T?
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  6. #6
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    Neither, I'm afraid. The AND works like this: p^q is true only if both p is true, and q is true. If either or both are false, then the AND function gives you a false. So, with that information, what do you get?
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  7. #7
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    So it is T, F, F, F?
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  8. #8
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    take (p and q)

    For (p,q)
    (1,1)--> 1
    (1,0)--> 0
    (0,1)--> 0
    (0,0)--> 0

    Think about it now.
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  9. #9
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    That's correct. What step should you take now?
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  10. #10
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    This is how I'd do it.

    Sorry I don't know how to do tables in LaTeX so I did it in paint, hope it's alright. I attached the file.

    Note the last 2 rows, they are vacuously true since p is F.

    Hope that helps... if you can any problems feel free to ask and I'll try explain.
    Attached Thumbnails Attached Thumbnails Truth Table-truth-table.jpg  
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