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Logic/ truth table

  1. Feb 6, 2010 #1
    I was given a truth table and I must write a wff with exactly two two-place connective. I am new to logic and don't know where to start. I need to find wff a), b), c) and d).

    C B A ..... wff a)
    T T T ........ T
    T T F ........ F
    T F T ........ T
    T F F ........ F
    F T T ........ T
    F T F ........ T
    F F T ........ T
    F F F ........ T

    A B C .....wff b)
    T T T ........ F
    T T F ........ T
    T F T ........ F
    T F F ........ F
    F T T ........ F
    F T F ........ T
    F F T ........ F
    F F F ........ T

    I have no clue on these first two. I tried many but they all seemed not to work.

    A B ..... wff c)
    T T ........ F
    T F ........ T
    F T ........ T
    F F ........ T

    I think I can do this one:
    this is equivalent to ~(A&B) but I need to use two two place connectives so I wrote ~(A&(B&B)) is this correct? Also the question didn't specify whether I can use "~". can I use it anyway?

    A ..... wff d)
    T ........ T
    F ........ T

    This one I can also manage but I'm not sure what is the right answer. This is equivalen to (Av~A) which I can write as ((A&A)v~A). However, I can also write ((A&A)->A) or ((A&A)<->A) aswell. I think there's a few more which is right?
  2. jcsd
  3. Feb 8, 2010 #2
    The first step in the algebraic way is to write the minterm for the variables for each row where you see T as the outcome you leave all variables where the income is T as is, and negate those where the variable is F

    for example
    TFT = T

    For a graphical solution you can draw the Karnaugh table of the function, and try to cover the T's with some (possibly overlapping) rectangular areas. You come up with the solution in a similar way, just now you can drop inputs where they are both T and F in the rectangle.

    I would say that the question did not say anything about one-place connectives, so using "~" should be okay.
    You are right that there can be more solutions to such a problem.
    I see no errors in your solutions above.
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