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English to symbolic form (transcription)

  1. Nov 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Hello!

    I got another problem:

    In order to attach the Mark 13 printer to the Lemon III computer, you must set eight "dip switches" in the computer according to the following rules. The switches are labeled a through h and are set to be either ON or OFF.

    (1) Neither a nor c is set the same as d.

    (2) b and g are different if and only if e and g are in the same positions.

    (3) g is OFF if d is OFF, but g is ON if b is OFF.

    (4) d is ON, unless e is the same as f.

    (5) b is not the same as a if either b or e is OFF.

    (6) g is OFF only if e is not the same as h.

    (7) b,f, and g are not all the same.

    How should the switches be set?

    2. Relevant equations



    3. The attempt at a solution

    I guess I need to transcribe them in symbolic form. Then create truth table and find values where the truth table is ON (i.e true) so that the Lemon III computer will work. (Maybe I will simplify all of the (1)-(7) before proceeding with truth tables).

    The problem is that I do not know how to transcribe them.

    First let me denote a,b,c, ...., f as a,b,c,....,f is ON.

    Now:

    (1) ~(a v c) <-> d

    (2) ~( b <-> d) -> (e <-> g)

    (3) (~d -> ~g) ^ (~b -> g)

    (4) (e <-> f) -> d

    (5) (~b v e) -> ~(b <-> a)

    (6) ~g -> ~(e <-> h)

    (7) ~(b<->f<->h)


    Are this transcriptions correct?
     
  2. jcsd
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