Liar or truth teller? Logic question 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.

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 $S = \
eg A \vee B$.

1. $A=1 \Rightarrow S = 1 \Rightarrow B = 1$
2. $A=0\Rightarrow S = 0 \Rightarrow S = 1 \vee B = 1$. Contradiction. So the are both truth tellers