Задачи по дискретной математике для контрольных и самостоятельных работ. Булевы функции. Васильев А.В - 21 стр.

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19. Проверить, является ли функция монотонной.
19.1. (x
1
∨ x
2
) ⊕ x
1
⊕ x
3
19.2. (x
1
↓ x
2
) ⊕ (x
2
↓ x
3
)
19.3. x
1
x
2
(x
1
→ x
3
)
19.4. (x
1
↓ x
3
) ∨ (x
1
| x
2
)
19.5. (x
2
→ x
3
) ⊕ (x
1
| x
3
)
19.6. (x
1
∼ x
1
) | (x
1
↓ x
2
)
19.7. x
1
∨ x
3
∨ (x
1
| x
2
)
19.8. (x
1
| x
2
) ↓
x
3
19.9. (x
1
∨ x
2
) → (x
2
∼ x
3
)
19.10. (x
3
→ x
1
) ⊕ x
1
x
2
19.11. (x
1
⊕ x
3
) | (x
1
↓ x
2
)
19.12. (x
2
→ x
1
) ∨ (x
1
↓ x
3
)
19.13. (x
1
↓ x
2
) → (x
1
⊕ x
3
)
19.14. (x
2
| x
3
) ↓ (x
1
⊕ x
3
)
19.15. (x
1
→ x
2
) | (x
2
∼ x
3
)
19.16. (x
1
∼ x
2
) ↓ (x
1
∨ x
3
)
19.17. (x
1
| x
2
) ⊕ x
2
x
3
19.18. (x
2
⊕ x
3
) ∼ (x
1
∨ x
3
)
19.19. (x
1
∨ x
3
) → (x
2
∨ x
3
)
19.20. (x
1
| x
2
) ∨ (x
2
∼ x
1
)
19.21. (x
1
∼ x
3
)(x
3
→ x
2
)
19.22. (x
1
x
3
) | (x
2
∨ x
3
)
19.23. (x
1
| x
2
) ∼ (x
2
| x
3
)
19.24. (x
2
∨ x
3
) ↓ (x
3
→ x
1
)
19.25. (x
1
∼ x
2
)(x
1
↓ x
3
)
19.26. (x
2
∨ x
3
) ↓ (x
1
↓ x
3
)
19.27. (x
1
| x
2
) ⊕ x
2
⊕ x
3
19.28. (x
2
→ x
1
) ↓ (x
1
∨ x
3
)
19.29. (x
2
⊕ x
3
) ↓ (x
1
⊕ x
2
)
19.30. (x
1
→ x
3
) | (x
2
| x
3
)
21
19. Проверить, является ли функция монотонной.
 19.1. (x1 ∨ x2 ) ⊕ x1 ⊕ x3
 19.2. (x1 ↓ x2 ) ⊕ (x2 ↓ x3 )
 19.3. x1 x2 (x1 → x3 )
 19.4. (x1 ↓ x3 ) ∨ (x1 | x2 )
 19.5. (x2 → x3 ) ⊕ (x1 | x3 )
 19.6. (x1 ∼ x1 ) | (x1 ↓ x2 )
 19.7. x1 ∨ x3 ∨ (x1 | x2 )
 19.8. (x1 | x2 ) ↓ x3
 19.9. (x1 ∨ x2 ) → (x2 ∼ x3 )
19.10. (x3 → x1 ) ⊕ x1 x2
19.11. (x1 ⊕ x3 ) | (x1 ↓ x2 )
19.12. (x2 → x1 ) ∨ (x1 ↓ x3 )
19.13. (x1 ↓ x2 ) → (x1 ⊕ x3 )
19.14. (x2 | x3 ) ↓ (x1 ⊕ x3 )
19.15. (x1 → x2 ) | (x2 ∼ x3 )
19.16. (x1 ∼ x2 ) ↓ (x1 ∨ x3 )
19.17. (x1 | x2 ) ⊕ x2 x3
19.18. (x2 ⊕ x3 ) ∼ (x1 ∨ x3 )
19.19. (x1 ∨ x3 ) → (x2 ∨ x3 )
19.20. (x1 | x2 ) ∨ (x2 ∼ x1 )
19.21. (x1 ∼ x3 )(x3 → x2 )
19.22. (x1 x3 ) | (x2 ∨ x3 )
19.23. (x1 | x2 ) ∼ (x2 | x3 )
19.24. (x2 ∨ x3 ) ↓ (x3 → x1 )
19.25. (x1 ∼ x2 )(x1 ↓ x3 )
19.26. (x2 ∨ x3 ) ↓ (x1 ↓ x3 )
19.27. (x1 | x2 ) ⊕ x2 ⊕ x3
19.28. (x2 → x1 ) ↓ (x1 ∨ x3 )
19.29. (x2 ⊕ x3 ) ↓ (x1 ⊕ x2 )
19.30. (x1 → x3 ) | (x2 | x3 )



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