Задачи по дискретной математике для контрольных и самостоятельных работ. Булевы функции. Васильев А.В - 20 стр.

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18. Проверить, является ли функция линейной.
18.1. ((x
3
⊕ x
1
) → (x
2
| x
1
))(x
3
⊕ x
2
)x
3
18.2. (x
1
⊕ (x
1
∼ x
3
)) → (x
2
∼ x
3
∼ (x
3
⊕ x
1
))
18.3. (x
2
∼ (x
3
x
2
)) ↓ x
1
18.4. x
1
→ (x
2
| (x
2
∨ x
3
))
18.5. (x
1
| (x
3
∨ x
2
)) ↓ x
1
18.6. (x
2
↓ x
3
)((x
1
⊕ x
2
) ↓ x
2
)
18.7. ((x
2
⊕ x
3
)x
1
) ∼
(x
2
↓ x
1
)
18.8. ((x
2
∼ x
3
) | x
3
) | x
1
18.9. (x
2
→ x
1
)(x
1
| x
2
)x
3
18.10. (x
2
| x
1
) ∼ (x
3
⊕ x
1
) ∼ (x
1
∨ x
3
)
18.11. (x
3
∼ (x
2
x
3
)) ⊕ ((x
2
∨ x
1
)x
1
)
18.12. (x
1
↓ x
2
) → (x
2
∨ x
3
)
18.13. ((x
1
→ x
3
) → (x
2
x
3
))
18.14. ((x
3
∼ x
1
) | x
1
) ↓ (x
3
| x
2
)
18.15. x
1
∨ (x
3
∼ (x
2
| x
1
))
18.16. (x
1
→ x
3
) → (x
2
∼ x
3
)
18.17. (x
2
→ x
3
) | (x
1
| x
2
)
18.18. (x
2
(x
2
∼ x
3
)) ⊕ x
3
⊕ (x
1
| x
2
)
18.19. (x
2
x
3
⊕ x
2
⊕ x
1
) ∼ (x
2
∨ x
3
)
18.20. (x
3
→ x
2
) | (x
3
∼ x
1
)
18.21. (x
3
∨ x
1
) ⊕ (x
2
↓ x
3
)
18.22. (x
3
| x
1
) | (x
1
↓ x
2
)
18.23. (x
3
⊕ x
3
) | (x
3
| x
2
)
18.24. (x
1
∼ (x
2
↓ x
3
)) ∼ (x
2
∨ x
3
)
18.25. (x
2
∨ x
1
)(x
3
→ x
2
)
18.26. ((x
1
⊕ x
2
) | x
3
) ⊕ (x
2
→ x
3
)
18.27. (x
3
∼ (x
2
x
3
)) | (x
2
| (x
2
∼ x
1
))
18.28. ((x
1
∨ x
3
) ∼ x
2
) | (x
2
x
3
⊕ x
3
)
18.29. (x
1
→ x
2
) ∨ (x
1
⊕ (x
2
∼ x
3
))
18.30. (x
1
↓ x
3
) ∼ (x
3
⊕ (x
1
∨ x
2
))
20
18. Проверить, является ли функция линейной.
 18.1. ((x3 ⊕ x1 ) → (x2 | x1 ))(x3 ⊕ x2 )x3
 18.2. (x1 ⊕ (x1 ∼ x3 )) → (x2 ∼ x3 ∼ (x3 ⊕ x1 ))
 18.3. (x2 ∼ (x3 x2 )) ↓ x1
 18.4. x1 → (x2 | (x2 ∨ x3 ))
 18.5. (x1 | (x3 ∨ x2 )) ↓ x1
 18.6. (x2 ↓ x3 )((x1 ⊕ x2 ) ↓ x2 )
 18.7. ((x2 ⊕ x3 )x1 ) ∼ (x2 ↓ x1 )
 18.8. ((x2 ∼ x3 ) | x3 ) | x1
 18.9. (x2 → x1 )(x1 | x2 )x3
18.10. (x2 | x1 ) ∼ (x3 ⊕ x1 ) ∼ (x1 ∨ x3 )
18.11. (x3 ∼ (x2 x3 )) ⊕ ((x2 ∨ x1 )x1 )
18.12. (x1 ↓ x2 ) → (x2 ∨ x3 )
18.13. ((x1 → x3 ) → (x2 x3 ))
18.14. ((x3 ∼ x1 ) | x1 ) ↓ (x3 | x2 )
18.15. x1 ∨ (x3 ∼ (x2 | x1 ))
18.16. (x1 → x3 ) → (x2 ∼ x3 )
18.17. (x2 → x3 ) | (x1 | x2 )
18.18. (x2 (x2 ∼ x3 )) ⊕ x3 ⊕ (x1 | x2 )
18.19. (x2 x3 ⊕ x2 ⊕ x1 ) ∼ (x2 ∨ x3 )
18.20. (x3 → x2 ) | (x3 ∼ x1 )
18.21. (x3 ∨ x1 ) ⊕ (x2 ↓ x3 )
18.22. (x3 | x1 ) | (x1 ↓ x2 )
18.23. (x3 ⊕ x3 ) | (x3 | x2 )
18.24. (x1 ∼ (x2 ↓ x3 )) ∼ (x2 ∨ x3 )
18.25. (x2 ∨ x1 )(x3 → x2 )
18.26. ((x1 ⊕ x2 ) | x3 ) ⊕ (x2 → x3 )
18.27. (x3 ∼ (x2 x3 )) | (x2 | (x2 ∼ x1 ))
18.28. ((x1 ∨ x3 ) ∼ x2 ) | (x2 x3 ⊕ x3 )
18.29. (x1 → x2 ) ∨ (x1 ⊕ (x2 ∼ x3 ))
18.30. (x1 ↓ x3 ) ∼ (x3 ⊕ (x1 ∨ x2 ))



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