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Таблица истинности ONLINE
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Таблица истинности для функции (C↓D)≡(C∧A∨D)≡((B|C←A)):
Промежуточные таблицы истинности:C↓D: C∧A: (C∧A)∨D: | C | A | D | C∧A | (C∧A)∨D | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | | 1 | 0 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 1 | 1 |
B|C: (B|C)←A: | B | C | A | B|C | (B|C)←A | | 0 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 1 | | 1 | 1 | 1 | 0 | 0 |
(C↓D)≡((C∧A)∨D): | C | D | A | C↓D | C∧A | (C∧A)∨D | (C↓D)≡((C∧A)∨D) | | 0 | 0 | 0 | 1 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 0 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 0 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
((C↓D)≡((C∧A)∨D))≡((B|C)←A): | C | D | A | B | C↓D | C∧A | (C∧A)∨D | (C↓D)≡((C∧A)∨D) | B|C | (B|C)←A | ((C↓D)≡((C∧A)∨D))≡((B|C)←A) | | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
Общая таблица истинности:| C | D | A | B | C↓D | C∧A | (C∧A)∨D | B|C | (B|C)←A | (C↓D)≡((C∧A)∨D) | (C↓D)≡(C∧A∨D)≡((B|C←A)) | | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: | C | D | A | B | F | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 1 |
F сднф = C∧¬D∧¬A∧¬B ∨ C∧¬D∧¬A∧B ∨ C∧¬D∧A∧B ∨ C∧D∧A∧B
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: | C | D | A | B | F | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 0 | 1 | 0 | | 1 | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | 1 |
F скнф = (C∨D∨A∨B) ∧ (C∨D∨A∨¬B) ∧ (C∨D∨¬A∨B) ∧ (C∨D∨¬A∨¬B) ∧ (C∨¬D∨A∨B) ∧ (C∨¬D∨A∨¬B) ∧ (C∨¬D∨¬A∨B) ∧ (C∨¬D∨¬A∨¬B) ∧ (¬C∨D∨¬A∨B) ∧ (¬C∨¬D∨A∨B) ∧ (¬C∨¬D∨A∨¬B) ∧ (¬C∨¬D∨¬A∨B)
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