SOLUTION: Solve the following using rules of replacement:
(E → T) ∧ (T → O), (¬O ∨ E)∴ (O ↔ T)
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Question 996085: Solve the following using rules of replacement:
(E → T) ∧ (T → O), (¬O ∨ E)∴ (O ↔ T)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
| Number | Statement | Lines Used | Reason |
|---|
| 1 | (E -> T) & (T -> O) | | |
| 2 | ~O v E | | |
| :. | O <--> T | | |
| 3 | E -> T | 1 | Simp |
| 4 | (T -> O) & (E -> T) | 1 | Comm |
| 5 | T -> O | 4 | Simp |
| 6 | ~~O -> E | 2 | MI |
| 7 | O -> E | 6 | DN |
| 8 | O -> T | 7,3 | HS |
| 9 | (O -> T) & (T -> O) | 8,5 | Conj |
| 10 | O <--> T | 9 | ME |
Acronyms/Abbreviations used
Simp = Simplification
Comm = Commutation
MI = Material Implication
ME = Material Equivalence
Conj = Conjunction
HS = Hypothetical Syllogism
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