Задачи по дискретной математике для контрольных и самостоятельных работ. Булевы функции. Васильев А.В - 8 стр.

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6. Эквивалентными преобразованиями привести формулу к ДНФ.
6.1. (x
2
∨ x
1
) | (x
3
∼ x
1
)
6.2. (x
1
| x
2
) ↓ (x
3
| x
1
)
6.3. (((x
2
x
1
) ∨ x
3
) → x
3
)
6.4. (((x
1
x
2
) → x
3
) ∨ x
2
)
6.5. ((x
2
∨ x
3
)x
1
) ∼ (x
1
∨ x
2
)
6.6. ((x
3
→ x
1
) ↓ x
2
) | x
1
6.7. x
2
∨ (x
1
| x
3
) ∨ (
(x
3
| x
2
) | x
1
)
6.8. ((x
2
| x
3
) ↓ x
3
) ↓ x
1
6.9. (x
3
→ (x
2
x
4
∼ x
1
)) ∨ x
2
6.10. ((x
2
→ x
1
)x
3
) | x
2
6.11. (((x
3
∼ x
2
) ∨ x
4
) ∨ x
1
)x
3
6.12. ((x
1
∨ x
2
) ∼ x
3
) ↓ x
4
6.13. (x
1
∨ (x
3
x
2
)) ⊕ x
2
6.14. (x
3
| x
2
) ∼ (x
1
∨ x
2
)
6.15. (x
1
→ x
3
) ↓ (x
2
→ (x
1
x
3
))
6.16. (x
3
⊕ x
2
) → (x
1
| x
3
)
6.17. (x
3
| x
1
) → (x
2
→ x
1
)(x
2
→ x
3
)
6.18. x
1
| ((x
2
⊕ x
3
)x
1
x
3
)
6.19. (x
1
∨ x
3
) → ((x
2
∨ x
1
) ⊕ x
2
)
6.20. ((x
3
| x
2
) ↓ (x
1
↓ x
2
)) | x
3
6.21. ((x
1
| x
2
)x
2
) ∨ ((x
2
| x
3
)x
2
)
6.22. (x
3
→ x
2
)x
1
⊕ x
3
6.23. (x
2
| x
3
)(x
1
| x
3
)x
2
6.24. (x
3
↓ x
1
) | (x
2
∼ x
1
)
6.25. (x
1
| x
2
) ↓ (x
3
↓ x
1
)
6.26. (x
1
↓ x
3
) → ((x
2
| x
3
)x
1
)
6.27. x
3
∼ (x
1
→ (x
2
↓ x
3
))
6.28. (x
1
→ x
2
) ⊕ (x
1
∼ x
3
)
6.29. (x
1
∨ x
2
) | ((x
1
x
2
) → (x
3
→ x
2
))
6.30. (x
1
⊕ x
2
⊕ x
3
) | x
1
8
6. Эквивалентными преобразованиями привести формулу к ДНФ.
 6.1. (x2 ∨ x1 ) | (x3 ∼ x1 )
 6.2. (x1 | x2 ) ↓ (x3 | x1 )
 6.3. (((x2 x1 ) ∨ x3 ) → x3 )
 6.4. (((x1 x2 ) → x3 ) ∨ x2 )
 6.5. ((x2 ∨ x3 )x1 ) ∼ (x1 ∨ x2 )
 6.6. ((x3 → x1 ) ↓ x2 ) | x1
 6.7. x2 ∨ (x1 | x3 ) ∨ ((x3 | x2 ) | x1 )
 6.8. ((x2 | x3 ) ↓ x3 ) ↓ x1
 6.9. (x3 → (x2 x4 ∼ x1 )) ∨ x2
6.10. ((x2 → x1 )x3 ) | x2
6.11. (((x3 ∼ x2 ) ∨ x4 ) ∨ x1 )x3
6.12. ((x1 ∨ x2 ) ∼ x3 ) ↓ x4
6.13. (x1 ∨ (x3 x2 )) ⊕ x2
6.14. (x3 | x2 ) ∼ (x1 ∨ x2 )
6.15. (x1 → x3 ) ↓ (x2 → (x1 x3 ))
6.16. (x3 ⊕ x2 ) → (x1 | x3 )
6.17. (x3 | x1 ) → (x2 → x1 )(x2 → x3 )
6.18. x1 | ((x2 ⊕ x3 )x1 x3 )
6.19. (x1 ∨ x3 ) → ((x2 ∨ x1 ) ⊕ x2 )
6.20. ((x3 | x2 ) ↓ (x1 ↓ x2 )) | x3
6.21. ((x1 | x2 )x2 ) ∨ ((x2 | x3 )x2 )
6.22. (x3 → x2 )x1 ⊕ x3
6.23. (x2 | x3 )(x1 | x3 )x2
6.24. (x3 ↓ x1 ) | (x2 ∼ x1 )
6.25. (x1 | x2 ) ↓ (x3 ↓ x1 )
6.26. (x1 ↓ x3 ) → ((x2 | x3 )x1 )
6.27. x3 ∼ (x1 → (x2 ↓ x3 ))
6.28. (x1 → x2 ) ⊕ (x1 ∼ x3 )
6.29. (x1 ∨ x2 ) | ((x1 x2 ) → (x3 → x2 ))
6.30. (x1 ⊕ x2 ⊕ x3 ) | x1



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