In a certain country every inhabitant is either a truth teller (who always tells the truth) or a liar (who always lies).
Traveling in this country you meet two of the inhabitants, Pat and Mel. Pat says, “If I am a truth teller, then Mel
is a truth teller.”
(a) Is Pat a truth teller or a liar?
(b) Is Mel a truth teller or a liar?
Provide mathematical justification for your answers.
Best Answer
Let $A = \text{'Pat is a truth teller'},\; B = \text{'Mel is a truth teller'}$. Then the statement is $S = A \to B$, that's equal to $S = \neg A \vee B$.