Some information about homework problem.

C'  is the conclusion - it is NOT a hypothesis
The problem CAN be done using our original statements (i.e. without replacing T by K)

Here’s what the lawyer said

If my client is guilty, then the knife was in the drawer

Either the knife was not in the drawer or Jason Pritchard saw the knife.

If the knife was not there on October 10, it follows that Jason Pritchard did not see the knife.

Furthermore, if the knife was there on October 10, then the knife was in the drawer and also the hammer was in the barn.

But we all know that the hammer was not in the barn.

Therefore, ladies and gentlemen of the jury, my client is innocent.

Here are the variables used

C client is guilty
K knife was in the drawer
T knife was there on October 10
S Jason Pritchard saw knife
H hammer was in the barn

1. C -> K hypothesis
2. K' v  S hypothesis
3. T' -> S' hypothesis
4. T -> (K ^ H) hypothesis
5. H' hypothesis

6. H’ v K’ 5. addition

7. (H ^ K)’ 6. DeMorgan’s

8. (K ^ H)’ 7. commutative

9. T’ 4,8 Modus Tollens

10. S’ 3,9 Modus Ponens

11. S v K’ 2 commutative

12 K’ 10,11 disjunctive syllogism

13 C’ 1,12 Modus Tollens