Discrete math: A, but not both B and C

1. Sep 17, 2015

Joseph1739

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. Sep 17, 2015

Joseph1739

Or is it: A(~B~C)

3. Sep 17, 2015

RUber

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:

4. Sep 18, 2015

HallsofIvy

Staff Emeritus
"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.

5. Sep 18, 2015

Merlin3189

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.

6. Sep 18, 2015

andrewkirk

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.