Задачи по дискретной математике для контрольных и самостоятельных работ. Булевы функции. Васильев А.В - 10 стр.

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8. Построить полином Жегалгина, используя эквивалентные преобразова-
ния.
8.1. x
2
∨ x
1
x
3
∨ x
3
8.2. (x
1
∨ x
3
)(x
2
(x
3
∨ x
2
)x
1
)
8.3. ((x
1
(x
2
∨ x
3
) ∨ x
3
)x
1
)x
2
8.4. (x
2
→ x
3
)(x
1
∨ x
2
)
8.5. x
2
x
1
∨ (x
3
⊕ x
1
)
8.6. (((x
2
∨
x
3
)x
1
)x
3
)
8.7. ((x
2
⊕ x
3
)x
1
) | ((x
2
| x
1
) ⊕ x
3
)
8.8. ((x
3
⊕ (x
2
→ (x
1
x
1
))x
3
) ⊕ x
2
)
8.9. (x
1
x
2
) → (x
4
∨ x
3
)
8.10. ((((x
4
⊕ x
2
) ∼ x
3
)x
1
) ∨ x
3
)
8.11. ((x
3
x
1
) ∼ x
2
)(x
1
∼ x
2
)((x
3
∼ x
2
)x
1
)
8.12. (x
1
∼ (x
3
⊕ x
2
)x
2
) ∼ (x
3
⊕ x
1
)
8.13. (x
1
⊕ ((x
2
→ x
3
) ⊕ x
1
)x
2
)
8.14. (x
3
∼ ((x
1
∨ x
2
) ⊕ x
2
) ∼ x
1
)
8.15. (x
4
⊕ (x
1
→ x
2
)x
1
) ↓ x
3
8.16. (((x
4
x
3
) ⊕ x
1
) → x
2
)
8.17. ((x
1
↓ (x
3
| x
4
)) | x
1
) ↓ x
2
8.18. ((x
2
(x
3
| x
1
) ∼ x
4
) ↓ x
3
)
8.19. (((x
4
| x
3
) → x
1
) ∼ x
2
)
8.20. (x
3
⊕ (x
1
∨ x
2
)x
3
)
8.21. (x
1
(x
2
∼ x
3
) ∨ x
1
x
2
) ⊕ x
3
8.22. (x
1
→ (x
3
(x
2
→ x
1
))x
2
)
8.23. (x
1
→ x
2
) ∨ (x
3
↓ x
3
)
8.24. x
2
→ (x
1
↓ (x
3
| x
1
))
8.25. x
3
⊕ (x
1
→ x
2
)(x
2
→ x
3
)
8.26. ((x
3
∨ x
1
) → x
2
) → x
1
8.27. (x
2
∼ x
1
) ↓ (x
3
↓ x
1
)
8.28. (x
2
∨ x
3
) | (x
3
→ x
1
)
8.29. (x
1
⊕ (x
2
∨ x
3
)) | x
3
8.30. x
1
(x
3
x
2
∨ (x
1
↓ x
2
))
10
8. Построить полином Жегалгина, используя эквивалентные преобразова-
   ния.
 8.1. x2 ∨ x1 x3 ∨ x3
 8.2. (x1 ∨ x3 )(x2 (x3 ∨ x2 )x1 )
 8.3. ((x1 (x2 ∨ x3 ) ∨ x3 )x1 )x2
 8.4. (x2 → x3 )(x1 ∨ x2 )
 8.5. x2 x1 ∨ (x3 ⊕ x1 )
 8.6. (((x2 ∨ x3 )x1 )x3 )
 8.7. ((x2 ⊕ x3 )x1 ) | ((x2 | x1 ) ⊕ x3 )
 8.8. ((x3 ⊕ (x2 → (x1 x1 ))x3 ) ⊕ x2 )
 8.9. (x1 x2 ) → (x4 ∨ x3 )
8.10. ((((x4 ⊕ x2 ) ∼ x3 )x1 ) ∨ x3 )
8.11. ((x3 x1 ) ∼ x2 )(x1 ∼ x2 )((x3 ∼ x2 )x1 )
8.12. (x1 ∼ (x3 ⊕ x2 )x2 ) ∼ (x3 ⊕ x1 )
8.13. (x1 ⊕ ((x2 → x3 ) ⊕ x1 )x2 )
8.14. (x3 ∼ ((x1 ∨ x2 ) ⊕ x2 ) ∼ x1 )
8.15. (x4 ⊕ (x1 → x2 )x1 ) ↓ x3
8.16. (((x4 x3 ) ⊕ x1 ) → x2 )
8.17. ((x1 ↓ (x3 | x4 )) | x1 ) ↓ x2
8.18. ((x2 (x3 | x1 ) ∼ x4 ) ↓ x3 )
8.19. (((x4 | x3 ) → x1 ) ∼ x2 )
8.20. (x3 ⊕ (x1 ∨ x2 )x3 )
8.21. (x1 (x2 ∼ x3 ) ∨ x1 x2 ) ⊕ x3
8.22. (x1 → (x3 (x2 → x1 ))x2 )
8.23. (x1 → x2 ) ∨ (x3 ↓ x3 )
8.24. x2 → (x1 ↓ (x3 | x1 ))
8.25. x3 ⊕ (x1 → x2 )(x2 → x3 )
8.26. ((x3 ∨ x1 ) → x2 ) → x1
8.27. (x2 ∼ x1 ) ↓ (x3 ↓ x1 )
8.28. (x2 ∨ x3 ) | (x3 → x1 )
8.29. (x1 ⊕ (x2 ∨ x3 )) | x3
8.30. x1 (x3 x2 ∨ (x1 ↓ x2 ))


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