Bob: Steve is lying
Steve: Bob is lying
Fred: Steve is lying or Bob is lying
"or" is inclusive
How would I approach this question? I honestly have no idea. I was thinking of making a truth table and assuming that each of them is saying the truth once and then going through the statements, but i'm not sure how I would handle the "or" bit within a truth table.
Just consider each assertion one by one, and its implications.
Therefore Steve is lying and Fred tells the truth => this is possible
Therefore Bob is lying and Fred tells the truth => this is possible
Either Steve or Bob is lying (those possibilities were already evaluated as possible) or both are lying. The latter case is impossible since we would then get that both are not lying, according to their respective assertions.
Then neither Steve nor Bob are lying which is impossible.
Conclusion:
Fred tells the truth, for sure, and either Bob or Steve is lying, but not both.
This can be written: Fred AND (Bob XOR Steve)
Note: XOR here is an exclusive OR, contrary to Fred's inclusive OR
Not really sure about this one, but I think
Fred AND (Bob OR Steve) are telling the truth
Because
One can assume that either Bob or Steve is telling the truth. Let's say Bob is telling the truth.
So if we assume Bob's statement "Steve is lying" is true, then Steve's statement "Bob is lying" is indeed false, because as we assumed, Bob is telling the truth.
They however cannot both be telling the truth because by their statements, if one of them is telling the truth then the other one is lying.
And they cannot both be lying because if one of them is lying, then that means the other is telling the truth.
So I think we can assume that only one of them is lying.
