SOLUTION: Use natural deduction to derive the conclusion in each problem. Use conditional proof: 1. S ⊃ (B ⊃ T) 2. N ⊃ (T ⊃ ∼B) / (S • N) ⊃ ∼B

Algebra ->  Proofs -> SOLUTION: Use natural deduction to derive the conclusion in each problem. Use conditional proof: 1. S ⊃ (B ⊃ T) 2. N ⊃ (T ⊃ ∼B) / (S • N) ⊃ ∼B      Log On


   

Question 1205227: Use natural deduction to derive the conclusion in each problem.

Use conditional proof:

1. S ⊃ (B ⊃ T)
2. N ⊃ (T ⊃ ∼B) / (S • N) ⊃ ∼B
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

I'll use an arrow in place of a horseshoe symbol.
I'll also replace the center dot with the ampersand symbol &
NumberStatementLine(s) UsedReason
1S --> (B --> T)
2N --> (T --> ~B)
:.(S & N) --> ~B
3S & NAssumption for Conditional Proof
4S3Simplification
5N3Simplification
6B --> T1, 4Modus Ponens
7T --> ~B2, 5Modus Ponens
8B --> ~B6, 7Hypothetical Syllogism
9~B v ~B8Material Implication
10~B9Tautology
11(S & N) --> ~B3 - 10Conditional Proof

Here is the list of the rules of inference and rules of replacement
https://www.algebra.com/algebra/homework/Conjunction/logic-rules-of-inference-and-replacement.lesson