The premises are:
(1) (q∧¬s)→r
(2) p
(3) p→q
(4) s→¬p

The argument, which proves r, is the following:
(5) q, because of ? applied to ? and ?
(6) ¬s, because of ? applied to ? and ?
(7) q∧¬s, because of ? applied to ? and ?
(8) r, because of ? applied to ? and ?

Question

The premises are:
(1) (q∧¬s)→r 
(2) p 
(3) p→q 
(4) s→¬p 

The argument, which proves r, is the following: 
(5) q, because of ? applied to ? and ?
(6) ¬s, because of ? applied to ? and ?
(7) q∧¬s, because of ? applied to ? and ?
(8) r, because of ? applied to ? and ?

anonymous · Answer

I got:
(5) q, because of modus ponens applied to 2 and 3
(6) ¬s, because of modus tollens applied to ? and 4
(7) q∧¬s, because of conjunction applied to 5 and 6
(8) r, because of modus ponens applied to ? and 7