I'm quite confused with creating proposition based on statements. Here's one:
p: "the card in Larry's left hand is an ace"
q: "the card in Larry's right hand is an ace"
r: "the card in Larry's left hand is a club"
s: "the card in Larry's right hand is a club"
write propositions using pqrs. My answer is after the (:)
-Larry has exactly one club: (r∧q) v (s∧p)
-If Larry has the ace of clubs in his left hand, then he doesn't have a club in his right hand : (r⇒¬s)
-Larry has at least one ace that is not a club : (p∧¬s) v (q∧¬r)
Am i interpreting it right? I'm curious. Any help is much appreciated.
The first is wrong: your translation says that either Larry has a club in his left hand and an ace in his right or he has a club in his right hand and an ace in his left -- which is compatible with his having e.g. a club in his left hand and also a club (the ace!) in his right.
The second is wrong: your translation says that if the card in Larry's left hand is a club, then the card in his right hand isn't a club. That doesn't translate the original, where the antecedent of the conditional mentioned an ace!
The third is wrong: (p∧¬s) v (q∧¬r). The translation is true when (p∧¬s) is true and that would be true when he has e.g. the ace of clubs in his left hand and the king of spades in his right, so he doesn't have at least one ace that is not a club.
There's no mystery to this kind of thing though it is easy to make slips (and I say this having fumbled my comment on the third part before re-editing! you just have to take it slowly and think).