1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    ABC
    TFT = T
    becomes
    [tex]A\overline{B}C[/tex]

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook