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Timothy asks,"Are you a knight if and only if there is gold on this island?"
Let K be the proposition that he is a knight,let G be the proposition that there is gold on the island,and let I be the proposition that K is true if and only if G is true.
Case 1:K is true,G is true.
K is true if and only if G is true,so I is true,and since K is true,he truthfully says,"Yes."
Case 2:K is true,G is false.
K is true if and only if G is false,so I is false,and since K is true,he truthfully says,"No."
Case 3:K is false,G is true.
K is true if and only if G is false,so I is false,and since K is false,he falsely says,"Yes."
Case 4:K is false,G is false.
K is true if and only if G is true,so I is true,and since K is false,he falsely says,"No."
If the native says yes,then there is gold,but if he says no,then there is not. |
