Question 1042390
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1. (PvQ)&R
2. (R&P)>S
3. (Q&R)>S
             Therefore, S
       | 4. ~S          Assumption for Indirect Proof
       | 5. R&(PvQ)     1, Commutation  
       | 6. R           5, Simplification
       | 7. ~(Q&R)      3,4 Modus Tollens
       | 8. ~Qv~R       7, DeMorgan's law  
       | 9. ~Rv~Q       8, Commutation
       |10. ~~R         6, Double negation
       |11. ~Q          9,10 Disjunctive syllogism 
       |12. PvQ         1, Simplification
       |13. QvP         12, Commutation  
       |14. P           13,11 Disjunctive syllogism
       |15. R&P         6,14 Conjunction
       |16. S           2,15 Modus ponens     
       |17. S&~S        16,4 Conjunction   <--(contradiction)
18. ~~S                 4-17 Indirect Proof
19. S                   18, Double negation 

Edwin</pre></b></font>