Задачи по дискретной математике для контрольных и самостоятельных работ. Булевы функции. Васильев А.В - 19 стр.

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17. Пользуясь принципом двойственности, построить формулу, реализую-
щую функцию, двойственную к заданной.
17.1. (x
1
∨ x
3
) ∼ ((x
1
| x
2
) ⊕ x
3
)
17.2. ((x
1
∨ x
2
) ↓ (x
1
∨ x
3
)) → x
2
17.3. (x
1
| x
2
) → ((x
2
⊕ x
3
) ∨ x
1
)
17.4. (x
1
⊕ x
2
) ∼ (x
1
x
3
)
17.5. (x
3
| x
2
) | ((x
3
↓ x
1
) ∨ x
3
)
17.6. x
3
| ((x
1
⊕ x
2
) ∼ x
3
)
17.7. (x
1
x
2
) ↓ ((x
3
x
2
) | x
3
)
17.8. x
1
x
3
∨ x
1
x
2
∨ (x
3
⊕ x
2
)
17.9. (x
2
→ (x
2
→ x
1
))(x
2
↓ x
3
)
17.10. (x
1
↓ (x
2
→ x
1
)) → (x
2
∨ x
3
)
17.11. ((x
1
⊕ x
2
) | (x
2
∨ x
1
)) ∼ (x
3
| x
2
)
17.12. (x
3
∨ (x
2
∼ x
1
)) → (
x
3
→ x
1
)
17.13. (x
3
x
1
) → ((x
1
⊕ x
2
) ∨ x
2
∨ x
1
)
17.14. (x
2
→ x
1
) | (x
3
∨ x
1
∨ (x
1
| x
2
))
17.15. (x
3
→ (x
3
| x
2
)) ∨ (x
1
⊕ x
2
)
17.16. (x
1
↓ x
3
) ∨ (x
2
∼ x
1
) ∨ (x
2
↓ x
3
)
17.17.
(x
1
∼ x
2
) ∨ x
2
∨ (x
2
→ x
3
)
17.18. ((x
1
↓ x
3
) → x
2
) ⊕ (x
1
→ x
2
)
17.19. x
1
→ ((x
2
→ x
3
) ↓ (x
3
⊕ x
2
))
17.20. x
1
⊕ (x
2
↓ ((x
1
↓ x
3
) → x
2
))
17.21. (x
1
→ x
2
) | ((x
1
| x
3
) ∨ x
2
)
17.22. ((x
1
∨ x
3
) →
(x
1
∨ x
2
)) ↓ x
2
17.23. x
1
⊕ (x
3
∼ (x
2
→ (x
1
→ x
3
)))
17.24. (x
2
| (x
1
∨ x
3
)) ↓ (x
2
∨ x
3
)
17.25. x
3
↓ ((x
2
| x
3
) ↓ x
1
)
17.26. x
3
((x
2
→ x
1
) | (x
1
↓ x
2
))
17.27. ((x
1
∨ x
2
)(x
2
∨ x
3
)) → (x
1
| x
3
)
17.28. (x
1
⊕ x
2
) ∨ ((x
2
⊕ x
3
) ∼ x
1
)
17.29. (x
2
| x
3
) ⊕ (x
1
↓ (x
3
⊕ x
1
))
17.30. (x
1
↓ x
3
) ∨ ((x
2
| x
3
) → x
2
)
19
17. Пользуясь принципом двойственности, построить формулу, реализую-
    щую функцию, двойственную к заданной.
 17.1. (x1 ∨ x3 ) ∼ ((x1 | x2 ) ⊕ x3 )
 17.2. ((x1 ∨ x2 ) ↓ (x1 ∨ x3 )) → x2
 17.3. (x1 | x2 ) → ((x2 ⊕ x3 ) ∨ x1 )
 17.4. (x1 ⊕ x2 ) ∼ (x1 x3 )
 17.5. (x3 | x2 ) | ((x3 ↓ x1 ) ∨ x3 )
 17.6. x3 | ((x1 ⊕ x2 ) ∼ x3 )
 17.7. (x1 x2 ) ↓ ((x3 x2 ) | x3 )
 17.8. x1 x3 ∨ x1 x2 ∨ (x3 ⊕ x2 )
 17.9. (x2 → (x2 → x1 ))(x2 ↓ x3 )
17.10. (x1 ↓ (x2 → x1 )) → (x2 ∨ x3 )
17.11. ((x1 ⊕ x2 ) | (x2 ∨ x1 )) ∼ (x3 | x2 )
17.12. (x3 ∨ (x2 ∼ x1 )) → (x3 → x1 )
17.13. (x3 x1 ) → ((x1 ⊕ x2 ) ∨ x2 ∨ x1 )
17.14. (x2 → x1 ) | (x3 ∨ x1 ∨ (x1 | x2 ))
17.15. (x3 → (x3 | x2 )) ∨ (x1 ⊕ x2 )
17.16. (x1 ↓ x3 ) ∨ (x2 ∼ x1 ) ∨ (x2 ↓ x3 )
17.17. (x1 ∼ x2 ) ∨ x2 ∨ (x2 → x3 )
17.18. ((x1 ↓ x3 ) → x2 ) ⊕ (x1 → x2 )
17.19. x1 → ((x2 → x3 ) ↓ (x3 ⊕ x2 ))
17.20. x1 ⊕ (x2 ↓ ((x1 ↓ x3 ) → x2 ))
17.21. (x1 → x2 ) | ((x1 | x3 ) ∨ x2 )
17.22. ((x1 ∨ x3 ) → (x1 ∨ x2 )) ↓ x2
17.23. x1 ⊕ (x3 ∼ (x2 → (x1 → x3 )))
17.24. (x2 | (x1 ∨ x3 )) ↓ (x2 ∨ x3 )
17.25. x3 ↓ ((x2 | x3 ) ↓ x1 )
17.26. x3 ((x2 → x1 ) | (x1 ↓ x2 ))
17.27. ((x1 ∨ x2 )(x2 ∨ x3 )) → (x1 | x3 )
17.28. (x1 ⊕ x2 ) ∨ ((x2 ⊕ x3 ) ∼ x1 )
17.29. (x2 | x3 ) ⊕ (x1 ↓ (x3 ⊕ x1 ))
17.30. (x1 ↓ x3 ) ∨ ((x2 | x3 ) → x2 )


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