Look at the argument below. Which of the following symbolic statements shows the set-up used to find the validity of the argument? If Mario studies hard, then he gets good grades. Mario got good grades. Therefore, Mario studied hard. p: Mario studies hard. q: Mario gets good grades. [(p → q) ∧ ~q] ∴ p [(p → q) → q] ∴ p [(p → q) ∧ q] ∴ q [(p → q) ∧ q] ∴ p

Question

Look at the argument below. Which of the following symbolic statements shows the set-up used to find the validity of the argument?  If Mario studies hard, then he gets good grades. Mario got good grades.  Therefore, Mario studied hard.    p: Mario studies hard.   q: Mario gets good grades. 	[(p → q) ∧ ~q]  ∴ p		[(p → q) → q]  ∴ p 	[(p → q) ∧ q]  ∴ q		[(p → q) ∧ q]  ∴ p

anonymous · Answer

It would be the last: 
(P arrow Q) ^ Q therefore P
However, the argument is wrong. The conditional states that if he studies, he gets good grades, it does not establish a relationship that good grades mean he studied. I'm not sure if that is required, but it would be fun to mention to correct your teacher.