Created
May 2, 2020 18:25
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(A ⇒ B) ∧ (¬A ⇒ C) = (A ∧ B) ∨ (¬A ∧ C)
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| (A ⇒ B) ∧ (¬A ⇒ C) | |
| = | |
| (¬A ∨ B) ∧ (¬¬A ∨ C) | |
| = | |
| (¬A ∨ B) ∧ (A ∨ C) | |
| = | |
| ((¬A ∨ B) ∧ A) ∨ ((¬A ∨ B) ∧ C) | |
| = | |
| ((¬A ∧ A) ∨ (B ∧ A)) ∨ ((¬A ∧ C) ∨ (B ∧ C)) | |
| = | |
| False ∨ (B ∧ A) ∨ (¬A ∧ C) ∨ (B ∧ C) | |
| = | |
| (A ∧ B) ∨ (¬A ∧ C) ∨ (B ∧ C) | |
| = | |
| (A ∧ B) ∨ (¬A ∧ C) ∨ (True ∧ B ∧ C) | |
| = | |
| (A ∧ B) ∨ (¬A ∧ C) ∨ ((A ∨ ¬A) ∧ B ∧ C) | |
| = | |
| (A ∧ B) ∨ (¬A ∧ C) ∨ ((A ∧ B ∧ C) ∨ (¬A ∧ B ∧ C)) | |
| = | |
| (A ∧ B) ∨ (¬A ∧ C) ∨ (A ∧ B ∧ C) ∨ (¬A ∧ C ∧ B) | |
| = | |
| (A ∧ B) ∨ (A ∧ B ∧ C) ∨ (¬A ∧ C) ∨ (¬A ∧ C ∧ B) | |
| = | |
| (A ∧ B ∧ True) ∨ (A ∧ B ∧ C) ∨ (¬A ∧ C ∧ True) ∨ (¬A ∧ C ∧ B) | |
| = | |
| ((A ∧ B ∧ True) ∨ (A ∧ B ∧ C)) ∨ ((¬A ∧ C ∧ True) ∨ (¬A ∧ C ∧ B)) | |
| = | |
| ((A ∧ B) ∧ (True ∨ C)) ∨ ((¬A ∧ C) ∧ (True ∨ B)) | |
| = | |
| ((A ∧ B) ∧ True) ∨ ((¬A ∧ C) ∧ True) | |
| = | |
| (A ∧ B) ∨ (¬A ∧ C) |
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