Answer: Alice has the prize
Step-by-step explanation:
[tex]\boxed{\begin{array}{c|c|c||l}\underline{Alice}&\underline{Bob}&\underline{Carol}&\underline{Prize}\\T&T&F&\text{Alice}\\T&F&F&\text{no possible answer}\\T&F&T&\text{no possible answer}\\F&T&T&\text{no possible answer}\\F&F&T&\text{no possible answer}\\F&T&F&\text{no possible answer}\end{array}}[/tex]
Line 1:
Alice: Bob doesn’t have the prize (T) ... either Alice or Carol
Bob: I don’t have the prize (T) ... either Alice or Carol
Carol: I have the prize (F) ... either Alice or Bob
Alice is true for all of them!
Line 2:
Alice: Bob doesn’t have the prize (T) ... either Alice or Carol
Bob: I don’t have the prize (F) ... Bob
Carol: I have the prize (F) ... either Alice or Bob
nobody satisfies all three statements.
Line 3:
Alice: Bob doesn’t have the prize (T) ... either Alice or Carol
Bob: I don’t have the prize (F) ... Bob
Carol: I have the prize (T) ... Carol
nobody satisfies all three statements.
Line 4:
Alice: Bob doesn’t have the prize (F) ... Bob
Bob: I don’t have the prize (T) ... either Alice or Carol
Carol: I have the prize (T) ... Carol
nobody satisfies all three statements.
Line 5:
Alice: Bob doesn’t have the prize (F) ... Bob
Bob: I don’t have the prize (F) ... Bob
Carol: I have the prize (T) ... Carol
nobody satisfies all three statements.
Line 6:
Alice: Bob doesn’t have the prize (F) ... Bob
Bob: I don’t have the prize (T) ... either Alice or Carol
Carol: I have the prize (F) ... either Alice or Bob
nobody satisfies all three statements.
