Needing help with line 4 is the entire problem :-) If this helps, take time to send 'thanks'... it is much appreciated:
1. P --> S Premise
2. P v Q Premise
3. Q --> R Premise
// Show S v R
4. ~P v S 1, Material Implication (MI)
5. S v Q 2,4 Resolution (RES)
6. ~Q v R 3, MI
7. R v S 5,6 RES
*** DONE ***
----
Alt Proof:
4. R v S 1,2,3 Constructive Dilemma (CD)
*** DONE ***
----
Alt Proof #2 (Conditional proof):
4.:: ~P Conditional proof (CP) assumption #1
5.:: Q 4,2 (RES)
6.:: R 5,3 Modus Ponens (MP) // we've shown R true if P false
7.:: P CP assumption #2
8.:: S 7,1 MP // we've shown S true if P true
9.:: S v R 4-8 Proof by Cases (PBC)
10. S v R 4-9 CP
*** DONE ***
In CPs, you are applying hypotheticals/scenarios and seeing what logically
follows; any interesting/useful conclusions can be extracted but the states of the variables do not change (for instance, one can NOT say R is true from line 6::, because that only followed from the ~P assumption on line 4::). I like to think of CPs as a way to see how the logic flows, without permenantly changing anything.
