How Do I solve this?

Question

Prove the following using RULES of INFERENCE/REPLACEMENT:

.1

1) P → Q 2)

2)R → S

3) דQVדS

——————

:.דP ד ٧R

Answer 1

Here's one way to do it:

1. P --> Q
2. R --> S
3. ~Q v ~S
4. ~Q --> ~P (1; Transposition)
5. ~S --> ~R (2; Transposition)

— — —

C. ~P v ~R (3-5; Constructive dilemma)

So each line has the line number, the statement, and then to the right if it's blank then it's given, otherwise it says how we inferred that line. So for example, line 4 says "~Q --> ~P" and then "(1; Transposition)" so that's the statement and then in parentheses, it tells us that it was inferred from line 1 using the rule of Transposition.

Hope that helps!

EDIT: tried to fix formatting