Help out Aladdin

If B's statement is false, then A has a treasure and hence A's statement is true. But it's impossible for the two statements to have different truth values. Thus B's statement is true, and consequently A's statement is true because the two statements must have equal truth values.

So A has a fatal trap, but there is at least one treasure among them. Thus B has the treasure.

Solution. Let’s consider a propositional language where a =“Trunk A contains the treasure” and b =“Trunk B contains the treasure”. 17 Propositional Logic + Obviously¬a =“Trunkacontainsatrap”(andsimilarlyfor¬b),sinceeach trunk either contains a treasure or a trap (exclusive or). Let’s formalize what Aladdin knows: • Formalization of the inscriptions: a∨b “At least one of these two trunks contains a treasure.” ¬a “A contains a trap” • Formalization of the problem: 1. “either both the inscriptions are true, or they are both false” (a∨b) ↔¬a What we can do is to verify whether there is any interpretation satisfying the formula in 1. : • The only interpretation satisfying 1. is: v(a) = F and v(b) = T • Thus Aladdin can open trunk B, being sure that it contains a treasure.

It is said that either both the statements are correct or both are false.Since we know that one contains treasure n other trap hence we can say that both the statements are correct hence the statement that A has a trap is correct so Aladdin opens B.