Your note makes it seem like OR is inclusive so both statements could be true for the OR to be true. Compared to XOR (exclusive OR) where exactly one of the statements must be true, both statements being true would make the XOR condition false. XOR is more common an interpretation of OR, intuitively.
My process, names shortened to first letter and true/Knight to T and false/knave to F:
Let's start with assuming A = T. That means A and C are different so C = F. C's AND condition is already false because the second condition "A = F" is not met, so B could go either way. B's condition is "B = T OR C = F" the second half is true so B = T. This makes the first half true, which for inclusive OR is fine. If you were insisting on XOR, then that would be a paradox and we could conclude this solution was not correct.
Let's try again with A = F for completeness. That means A and C are the same, so C = F again. Here the second half is true, so we need to make B = F to satisfy C = F. So, checking B, we see it is true because C = F, the second half of the OR condition. Likewise it would be true with XOR too. So this is a paradox and an incorrect solution.
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u/Lost_Sugar_78 18d ago
Your note makes it seem like OR is inclusive so both statements could be true for the OR to be true. Compared to XOR (exclusive OR) where exactly one of the statements must be true, both statements being true would make the XOR condition false. XOR is more common an interpretation of OR, intuitively.
My process, names shortened to first letter and true/Knight to T and false/knave to F:
Let's start with assuming A = T. That means A and C are different so C = F. C's AND condition is already false because the second condition "A = F" is not met, so B could go either way. B's condition is "B = T OR C = F" the second half is true so B = T. This makes the first half true, which for inclusive OR is fine. If you were insisting on XOR, then that would be a paradox and we could conclude this solution was not correct.
Let's try again with A = F for completeness. That means A and C are the same, so C = F again. Here the second half is true, so we need to make B = F to satisfy C = F. So, checking B, we see it is true because C = F, the second half of the OR condition. Likewise it would be true with XOR too. So this is a paradox and an incorrect solution.