SOLUTION: please use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1. T ⊃ R
2. T ⊃ ~R / ~T
Algebra.Com
Question 1207022: please use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1. T ⊃ R
2. T ⊃ ~R / ~T
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
I'll use an arrow symbol in place of the horseshoe symbol.
| Number | Statement | Line(s) Used | Reason |
| 1 | T --> R | | |
| 2 | T --> ~R | | |
| :. | ~T | | |
| 3 | ~~R --> ~T | 1 | Transposition |
| 4 | R --> ~T | 3 | Double Negation |
| 5 | T --> ~T | 1, 4 | Hypothetical Syllogism |
| 6 | ~T v ~T | 5 | Material Implication |
| 7 | ~T | 6 | Tautology |
The Rules of Inference and Rules of Replacement are shown here
RELATED QUESTIONS
PLease use all 18 rules of natural deduction to derive the conclusion (/), thanks.
1.... (answered by mccravyedwin,math_tutor2020)
Use Indirect Proof and the 8 Rules of Implication and the 10 Rules of
Replacement of... (answered by Edwin McCravy)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by jim_thompson5910)
Use natural deduction to derive the conclusion of the following arguments. Do not use... (answered by math_helper)
Use the inference rules to derive the conclusion
1. T ⊃ O
2. R v ~O
3. ~R/~T
(answered by Plocharczyk,Edwin McCravy)
Please use the 18 rules of natural deduction, the 4 instantiation and generalization... (answered by Edwin McCravy,math_tutor2020)
Use natural deduction to derive the conclusion in each problem.
Use conditional... (answered by math_tutor2020)
use the inference rules, replacement rules, indirect proof and/or conditional proof to... (answered by mccravyedwin,Edwin McCravy)
Please use the 18 rules of natural deduction, the 4 instantiation and generalization... (answered by ElectricPavlov)