There is a land where every inhabitant is either a day-knight or a night-knight. Day-knights tell the truth in the day and lie at night. Night-knights lie in the day and tell the truth at night. An inhabitant says, "Either I am a day-knight or it is day." Is the inhabitant a day-knight or a night-knight, and is it day or night?
As a logical disjunction is TRUE if either operand is TRUE,
then the inhabitant must be a day-knight and it is day.
If he were a day-knight and it were night, he would need be
telling a falsehood. In order for that to have occurred, both
operands would need be FALSE. As the first operand is "I am a
day-knight", which is TRUE, both operands would not be FALSE.
Thus, he could not be a day-knight and it being night.
The same goes if he were a night-knight and it were day. He
would need be telling a falsehood by definition of night-knight.
As both operands of the statement would need be FALSE, and the latter operand "it is day" would be TRUE, he could not be a night-knight and it being day.
If he were a night-knight and it were night, by definition of
night-knight he would need be making a TRUE statement. For this to occur, at least one operand must be TRUE. As both "I am a day-knight" and "it is day" would be FALSE, he could not be a night-knight and it were night.
The only case that fulfills the definition is where he is a day-knight and it is day.
Posted by Dej Mar
on 2012-07-02 12:33:18