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Simple Boolean Algebra / Propositional Logic Question

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Produce the given truth table (given below as well as in a neater version in the attached Excel document) using the Boolean operators AND, OR, and/or NOT:

    A (Input 1) B (Input 2) O (Output)
    1 1 0
    1 0 0
    0 1 1
    0 0 0



    2. Relevant equations

    None; since AND, OR, and NOT are presumed knowledge.

    3. The attempt at a solution

    I tried taking the AND and OR of it and then taking the XOR (A AND (NOT B) OR ((NOT A) AND B)) of those results but that led me nowhere. I honestly have no idea how to proceed. Any help would be greatly appreciated. Feel free to express the solution (or parts thereof) in the conventional notation of logical conjunctions/disjunctions ([itex]\wedge[/itex] / [itex]\vee[/itex]) and negations ([itex]\neg[/itex]), if you prefer. Thanks!

    P.S.

    I am not using this for homework or coursework. It is actually for a circuit I'm building in the computer game Minecraft! So feel free to just give me a fully worked solution. :smile:
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Aug 23, 2011 #2

    Dick

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    Homework Helper

    Probably best if you figure it out yourself, even if it's not a homework. This is after all the homework section. (A AND B) has one true outcome just like your example but it's in the wrong place. So that's a good place to start. Try putting a 'NOT' on the A or B.
     
  4. Aug 23, 2011 #3
    I just figured it out. I was overcomplicated things unnecessarily. I see now that the answer is: [itex]\neg[/itex]A [itex]\wedge[/itex] B.

    While I do thank you for your help, I would like to point out that the fact that: "This is after all the homework section", does not in any way preclude your ability to do it for me. That being said, I do agree with your general desire for the OP to figure things out themselves, with as minimal aid as possible.
     
  5. Aug 23, 2011 #4
    This thread is now solved. It can be locked. Thanks.
     
  6. Aug 23, 2011 #5

    Dick

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    Science Advisor
    Homework Helper

    Being in the homework section does preclude just giving an answer. At least in my mind. But you did just fine on your own. Good work.
     
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