Artificial intelligent assistant

Validity of Contraposition. Contraposition says: $$ P \implies Q \iff \neg Q \implies \neg P $$ What if P means "Santa Claus is in town" and Q means "I am in town"? It would mean: If Santa Claus is in town, then I am in town. Due to contraposition it also means: If I am not in town, then Santa Clause is also not in town. So, I am the reason why Santa Clause is not in town. Based on this, P causes Q and vice versa. But I think there could be more than one reason why P does not happen other than that Q does not happen. The reason why Santa Clause is not in town could be because of many other reasons and not just because I am not in town.Or what is my misunderstanding here?

Don't think of "cause" here - it doesn't generalize that easily.

Consider the statements P = "The Aggies win the next football game" and Q = "I win the bet I made with Tom." So, $P \implies Q$ means "If the Aggies win the next football game, then I win the bet I made with Tom." Consider the contrapositive: "If I lost the bet I made with Tom, then the Aggies lost the next football game." Think of this: The Aggies win, I win my bet. But if I lost my bet, then certainly the Aggies lost. The same reasoning, huh?

But try this, if I won the bet, does that mean the Aggies won? Not necessarily. Fallacy of the converse.

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