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)

Algebra ->  Proofs -> 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)       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Here is one way to do a proof derivation to get the conclusion
NumberStatementLines UsedReason
1R v ~S
2~R v T
3T --> (S & U)
:.S = T
4~S v R1Commutation
5~~S --> R4Material Implication
6S --> R5Double Negation
7~~R --> T2Material Implication
8R --> T7Double Negation
9S --> T6,8Hypothetical Syllogism
10~T v (S & U)3Material Implication
11(~T v S) & (~T v U)10Distribution
12~T v S11Simplification
13~~T --> S12Material Implication
14T --> S13Double Negation
15(S --> T) & (T --> S)9,14Conjunction
16S = T15Material Equivalence