Not much sense - I think you are trying to ask how to write (combine?) three logical notions. While programming notation may be better there, I'm thinking best just keep to English; I think you're trying to say:
1. If A and B are both true, C must be false
2. If B and C are both true, A must be false
3. If C and A are both true, B must be false
Note how those statements are only the one-way version. If that is all, they are equivalent to "not (A and B and C)", i.e. A, B and C are never all true together. If you don't like the brackets, it expands to become "not A or not B or not C".
That limits them to 2 being true at most, but also admits possibly 1 or none being true. If you meant those statements to be two-way, in effect generating three more logical claims, it limits them further such that exactly 2 must be true at all times.
I can't imagine a more concise logical statement for that than listing the three possibilities, i.e. "(A and B and not C) or (B and C and not A) or (C and A and not B)".
SithEmpire 0 points 3 months ago
Not much sense - I think you are trying to ask how to write (combine?) three logical notions. While programming notation may be better there, I'm thinking best just keep to English; I think you're trying to say:
1. If A and B are both true, C must be false
2. If B and C are both true, A must be false
3. If C and A are both true, B must be false
Note how those statements are only the one-way version. If that is all, they are equivalent to "not (A and B and C)", i.e. A, B and C are never all true together. If you don't like the brackets, it expands to become "not A or not B or not C".
That limits them to 2 being true at most, but also admits possibly 1 or none being true. If you meant those statements to be two-way, in effect generating three more logical claims, it limits them further such that exactly 2 must be true at all times.
I can't imagine a more concise logical statement for that than listing the three possibilities, i.e. "(A and B and not C) or (B and C and not A) or (C and A and not B)".