There were 3 people J, P, A. Only 2 people brought gifts to the party. If J brought a gift to the party, proof that P or A did not brought the gift.
What I can think about this sentence is: $ J, P \rightarrow ¬A, A \rightarrow ¬P \vDash ¬A \lor ¬P $
But with these premises and conclusion, I can't proof it in semantic way or proof theory by applying CNF to derive empty clause. I would like to ask for help that what should be the right premises and conclusion?
Thank you very much for any helps that you may provide.
Updated from suggestions:
$J, ¬(J\land P \land A) \vDash ¬A \lor ¬P $
$J, ¬(J \land (P \land A)) \vDash ¬A \lor ¬P $
$J, ¬J \lor ¬(P \land A) \vDash ¬A \lor ¬P $
$J, ¬J \lor ¬P \lor ¬A \vDash ¬A \lor ¬P $
Apply resolution to derive empty clause.
$J, ¬J \lor ¬P \lor ¬A, ¬(¬A \lor ¬P) \vdash $ Empty Clause
$J, ¬J \lor ¬P \lor ¬A, A \land P \vdash $ Empty Clause
Empty Clause $ \vdash $ Empty Clause
Thank you for all helps.