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

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) (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 &

Number		Statement	Line(s) Used	Reason
1		S --> (B --> T)
2		N --> (T --> ~B)
:.		(S & N) --> ~B
	3	S & N		Assumption for Conditional Proof
	4	S	3	Simplification
	5	N	3	Simplification
	6	B --> T	1, 4	Modus Ponens
	7	T --> ~B	2, 5	Modus Ponens
	8	B --> ~B	6, 7	Hypothetical Syllogism
	9	~B v ~B	8	Material Implication
	10	~B	9	Tautology
11		(S & N) --> ~B	3 - 10	Conditional 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

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