ngs 1. Complete a direct derivation (also called a "direct proof") for each of the following arguments, showing that it is valid. You will need the rules modus ponens, modus tollens, and double negation. 1. Premises: -Q. (QS). Show: S. 2. Premises: (S-Q), ( PS), --P. Show: -Q. 3. Premises: ( TP), ( QS), ( ST), -P. Show: -Q. 4. pkemises: R, P. (P (R Q)). Show: Q. 5. Premises: (( RS) Q), -Q. (-( RS) V). Show: V. 6. Premises: (P ( QR)), -( QR). Show: -P. 7. Premises: (-( QR) P), -P, Q. Show: R. 8. Premises: P. ( PR), (P (R Q)). Show