Question 1193789: H ≡ N
H ∨ N
H ⊃ (N ⊃ U) / U
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Here is one way to do the derivation. There are probably more shorter efficient paths to take.
| Number | Statement | Line(s) Used | Reason | | 1 | H = N | | | | 2 | H v N | | | | 3 | H -> (N -> U) | | | | :. | U | | | | 4 | (H -> N) & (N -> H) | 1 | Material Equivalence | | 5 | H -> N | 4 | Simplification | | 6 | N -> H | 4 | Simplification | | 7 | ~~H v N | 2 | Double Negation | | 8 | ~H -> N | 7 | Material Implication | | 9 | ~H -> H | 8, 6 | Hypothetical Syllogism | | 10 | ~~H v H | 9 | Material Implication | | 11 | H v H | 10 | Double Negation | | 12 | H | 11 | Tautology | | 13 | N v H | 2 | Commutation | | 14 | ~~N v H | 13 | Double Negation | | 15 | ~N -> H | 14 | Material Implication | | 16 | ~N -> N | 15, 5 | Hypothetical Syllogism | | 17 | ~~N v N | 16 | Material Implication | | 18 | N v N | 17 | Double Negation | | 19 | N | 18 | Tautology | | 20 | N -> U | 3, 12 | Modus Ponens | | 21 | U | 20, 19 | Modus Ponens |
I used arrows in place of horseshoe symbols.
Also, I used a regular equal sign in place of the triple equal sign.
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