SOLUTION: Premises: 1.) V->H 2.) ~V->S 3.) ~H -> ~S Conclusion: /H

Algebra ->  Proofs -> SOLUTION: Premises: 1.) V->H 2.) ~V->S 3.) ~H -> ~S Conclusion: /H      Log On


   

Question 969536: Premises:
1.) V->H
2.) ~V->S
3.) ~H -> ~S
Conclusion:
/H
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Premises:
1.) V->H
2.) ~V->S
3.) ~H -> ~S
Conclusion:
/H
4. ~~S->~~H       contrapositive, 3 
5. S->H           double negation, 4
6. ~V->H          hypothetical syllogism 2,5 
7. ~H->~~V        contrapositive, 6  
8. ~H->V          double negation, 7
9. ~H->~V         contrapositive, 1
10. V or ~V       tautology
11. H or H        constructive dilemma, 1,6,10

              Here's an explanation of step 11:
                  constructive dilemma says: p->q,r->s,(p or r), / (q or s)
                  we substitute p=V, q=H, r=~V, s=H      
                                             V->H,~V->H,(V or ~V), / (H or H)
                                                1,    6,       10, /   11
12. H             simplification (or idempotent), 11

Edwin