Our adventuring party is exploring a forest, and along the way we run across a c

Question

Our adventuring party is exploring a forest, and along the way we run across a camp of paladins and rogues. The paladins always tell the truth, and the rogues always lie. We cannot distinguish them on sight (they all wear the same armor) We're looking for treasure (of course), so we ask the guard at the gate if there is treasure hidden in the forest. She says the following statement: If I am a paladin, then there is treasure hidden in the forest. Using formal logic, determine if the guard is a paladin or a rogue and if there is treasure in the forest. If it's helpful, you can use a truth table to support your answer (but you don't have to).

Explanation / Answer

Hi,
Lets look at the statement given
if there is treasure hidden in the forest. She says the following statement: If I am a paladin, then there is treasure hidden in the forest
this is an implication statement i.e A->B
where A - guard is a paladian and B-> treasure is hidden in forest
lets draw the truth table of A->B

As, you can see from above, the statement can only be false when A is T and B is F,
since rogues always lie, lets assume the guard is rogue, so the statement is false(as he lies always), so that mean A should be T, i.e guard should be paladin, which is a contradiction,  
which means, the guard is a paladin
and now, if the guard is a paladin, and A->B is also true(since he always tells truth) that means from the truth table, B also has to be true, therefore the guard is a paladin and treasure is hidden in forest
Thumbs up if this was helpful, otherwise let me know in comments

A B A->B T T T T F F F T T F F T

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