SOLUTION: please use all 18 rules of natural deduction to derive the conclusion (/), thanks. 1. T ⊃ R 2. T ⊃ ~R / ~T

Algebra ->  Proofs -> SOLUTION: please use all 18 rules of natural deduction to derive the conclusion (/), thanks. 1. T ⊃ R 2. T ⊃ ~R / ~T      Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!

I'll use an arrow symbol in place of the horseshoe symbol.
NumberStatementLine(s) UsedReason
1T --> R
2T --> ~R
:.~T
3~~R --> ~T1Transposition
4R --> ~T3Double Negation
5T --> ~T1, 4Hypothetical Syllogism
6~T v ~T5Material Implication
7~T6Tautology


The Rules of Inference and Rules of Replacement are shown here