SOLUTION: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof. 1. R v ~S 2. ~R v T 3. T ⊃ (S • U)

Question 1132243: Use natural deduction to derive the conclusion of the following arguments. Do not use conditional proof or indirect proof.
1. R v ~S
2. ~R v T
3. T ⊃ (S • U)
Conclusion: S ≡ T
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Here is one way to do a proof derivation to get the conclusion

Number	Statement	Lines Used	Reason
1	R v ~S
2	~R v T
3	T --> (S & U)
:.	S = T
4	~S v R	1	Commutation
5	~~S --> R	4	Material Implication
6	S --> R	5	Double Negation
7	~~R --> T	2	Material Implication
8	R --> T	7	Double Negation
9	S --> T	6,8	Hypothetical Syllogism
10	~T v (S & U)	3	Material Implication
11	(~T v S) & (~T v U)	10	Distribution
12	~T v S	11	Simplification
13	~~T --> S	12	Material Implication
14	T --> S	13	Double Negation
15	(S --> T) & (T --> S)	9,14	Conjunction
16	S = T	15	Material Equivalence

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