Discrete math: A, but not both B and C

[Joseph1739]

Homework Statement

Translate: A, but not both B and C

Homework Equations

AB = A and B
A+B = A or B
~ = not

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).

 

[Joseph1739]

Or is it: A(~B~C)

 

[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:

The only other solution I can think of is A~(BC) = A(~B+~C).

 

[HallsofIvy]

"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.

 

[Merlin3189]

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).

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.

 

[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.