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Discrete math: A, but not both B and C

  1. Sep 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Translate: A, but not both B and C

    2. Relevant equations
    AB = A and B
    A+B = A or B
    ~ = not

    3. The attempt at a solution
    I'm not sure if my translation of this is correct:
    A(B XOR C)
    The statement is throwing off my translation because usually when I use XOR, it means B or C, but not both.
    So is B or C, but not both = not both B and C?
    The only other solution I can think of is A~(BC) = A(~B+~C).
     
  2. jcsd
  3. Sep 17, 2015 #2
    Or is it: A(~B~C)
     
  4. Sep 17, 2015 #3

    RUber

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    One of your options is correct.
    A and not both B and C means that no matter what A. So in all of your options, I see A, so this is right.
    Not both B and C means that it is possible to have a) neither B nor C, b) C and not B, c) B and not C. ... It really means the only thing it cannot be is B and C.
    So my vote goes to:
     
  5. Sep 18, 2015 #4

    HallsofIvy

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    "not both B and C" could mean "B but not c" or "C but not B" or "neither B nor C". You have to cover all three of those.
     
  6. Sep 18, 2015 #5

    Merlin3189

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    I would say that your translation, " B or C, but not both = not both B and C " is correct.

    So XOR is, as you say, not the form you require.
     
  7. Sep 18, 2015 #6

    andrewkirk

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    Have they taught you how to use truth tables Joseph?
    As Ruber says, one of the solutions you have considered in posts 1 and 2 is correct. If you are not confident of which one it is, writing out the truth tables for each of them, and for your natural language understanding of 'A, but not both B and C', will enable you to make sure of which one exactly matches the natural language version.

    As there are only three Boolean variables, the truth table has only 8 rows, so does not take long to construct.
     
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