True Output

How do i prove this is a tautology without using truth tables?

(q ^ p) --> ( q --> p)

Public Comments

1. Find the opposite : It can't be a tautology if there's a F value. The only time a->b is false is when a is T and b is F. q ^ p = T and q-->p is F (AND) can only be T if both values are T. So p=T and q=T. (IF) can only be F if q=T and p=F. It is not possible for both of these case to occur. Therefore, this statement can never be False. It is a tautology.
2. You can answer using proof of validity 1.q^p/ therefore q-->p 2. q/ therefore p RCP 3. p Modus Ponens of 1 and 2 4. q-->p RCP from 2-3