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.
| Number | Statement | Line(s) Used | Reason | | 1 | S --> (L & M) | | | | 2 | M --> (L --> R) | | | | :. | S --> R | | | | 3 | (M & L) --> R | 2 | Exportation | | 4 | (L & M) --> R | 3 | Commutation | | 5 | S --> R | 1, 4 | Hypothetical Syllogism |
The Rules of Inference and Rules of Replacement are shown here
|
|
|
