SOLUTION: PLease use all 18 rules of natural deduction to derive the conclusion (/), thanks. 1. S ⊃ (L • M) 2. M ⊃ (L ⊃ R) / S ⊃ R

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Question 1207017: PLease use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1. S ⊃ (L • M)
2. M ⊃ (L ⊃ R) / S ⊃ R
Found 2 solutions by mccravyedwin, math_tutor2020:
Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!

1. S ⊃ (L • M)
2. M ⊃ (L ⊃ R) / S ⊃ R

          |3. S          assumption for conditional proof
          |4. L • M    1,3, modus ponens
          |5. M • L      4, commutation
          |6. M          5, simplification
          |7. L ⊃ R    2,6, modus ponens
          |8. L          4, simplification
          |9. R        7,8, modus ponens
10. S ⊃ R    lines 3-9 for conditional proof

Edwin
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

I'll use an arrow symbol in place of the horseshoe symbol.
Also, I'll use an ampersand in place of a dot.

Here is one way to do the derivation.
NumberStatementLine(s) UsedReason
1S --> (L & M)
2M --> (L --> R)
:.S --> R
3(M & L) --> R2Exportation
4(L & M) --> R3Commutation
5S --> R1, 4Hypothetical Syllogism


The Rules of Inference and Rules of Replacement are shown here
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