LJ (WJ ~S) ~PJ (W V ~L) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. ~PJ (LO~S) ~P LO~S L WD ~S WV ~L ~LVW ~~L W ~S /~PJ (LO~S

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Lj Wj S Pj W V L 1 2 3 4 5 6 7 8 9 10 11 12 Pj Lo S P Lo S L Wd S Wv L Lvw L W S Pj Lo S 1 (7.17 KiB) Viewed 36 times

You can use conditional proof when you need to prove aconditional. If the conclusion of an argument is a conditional,then you should consider using conditional proof to obtain theconclusion. To do this, assume the conditional's antecedent tobegin a new indented sequence, and try to prove the conditional'sconsequent within the scope of the same indented sequence. If yousucceed in obtaining the conditional's consequent, then you candischarge the indented sequence to conclude the conditional on thenext, non-indented line following the indented sequence.You can use conditional proof as part of a larger proof, if youneed a conditional to perform a subsequent step. Suppose, forexample, that you have the proposition (Z ⊃ R) ⊃ F as a givenpremise. In order to use modus ponens (MP), you also need theantecedent Z ⊃ R, which is a conditional. Since Z ⊃ R is aconditional, you can try to use conditional proof to obtain Z ⊃ Rby assuming the antecedent Z and trying to obtain the consequent Rwithin the scope of the indented sequence. Once you have dischargedthe conditional sequence to obtain Z ⊃ R, you can proceed to usemodus ponens to obtain F on a subsequent line.You can also use one conditional proof sequence within the scope ofanother conditional proof sequence. When you are working within aconditional proof sequence that is inside another indentedsequence, you can use lines from the outer sequence asjustification for new lines in the inner sequence. But you cannotuse lines from any conditional or indirect sequences that havealready been discharged as justification for new lines.For example, suppose that you are trying to prove the conclusion Z⊃ (R ⊃ F). You can try to obtain this conclusion using twoconditional proofs, one inside the other. The conclusion is aconditional with Z as its antecedent, so assume Z on an indentedline. Then, try to prove R ⊃ F within the scope of the sameindented sequence. Since R ⊃ F is a conditional, you can useanother conditional proof to try to obtain R ⊃ F. Within the firstindented sequence, begin a new indented sequence (indented furtherthan the first sequence) assuming R. Then, try to obtain F withinthe scope of the inner sequence. If you succeed, you can dischargethe inner indented conditional sequence to obtain R ⊃ F within thescope of the outer conditional sequence. Then you can discharge theouter conditional sequence to obtain the overall conclusion Z ⊃ (R⊃ F) on a non-indented line to conclude the proof.
LJ (WJ ~S) ~PJ (W V ~L) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. ~PJ (LO~S) ~P LO~S L WD ~S WV ~L ~LVW ~~L W ~S /~PJ (LO~S)