Задачи по дискретной математике для контрольных и самостоятельных работ. Булевы функции. Васильев А.В - 25 стр.

UptoLike

ВУЗ: 

КФУ | Казань

Составители: 

Рубрика: 

23. Из системы функций выделить все базисы A.
23.1. A = {x
1
∼ x
2
, (x
1
| x
2
) ⊕ (x
3
∨ x
1
), x
2
∼ (x
3
⊕ x
1
), x
3
→ (x
1
∼ x
2
)}
23.2. A = {x
1
∼ x
2
, (x
3
⊕ x
1
) ↓ (x
2
| x
3
), x
1
∨ x
2
∨ x
3
, (x
3
x
2
) ∨ (x
2
⊕ x
3
)}
23.3. A = {(x
1
↓ x
3
) ∨ x
2
, (x
3
↓ x
1
) | (x
2
→ x
1
), x
1
∨ x
2
∨ (x
3
| x
1
),
(x
1
| x
2
) ∨ (x
2
∼ x
1
)}
23.4. A = {x
1
| (x
2
→ x
1
), (x
2
x
1
) → x
3
, x
1
⊕x
2
⊕x
3
, (x
3
→ x
2
) ∼ (x
1
⊕x
2
)}
23.5. A = {(x
1
∼ x
2
), (x
1
⊕ x
2
) ∨ x
3
, (x
1
| x
2
)x
1
, x
1
→ (x
2
∼ x
3
)}
23.6. A = {(x
3
| x
1
) ∨ x
2
∨ x
1
, x
2
⊕ (x
1
∨ x
2
), (x
2
| x
1
) | x
3
,
(x
1
↓ x
3
) ∨ (x
2
→ x
3
)}
23.7. A = {x
3
(x
1
∼ x
2
), x
1
⊕ x
2
⊕ x
3
⊕ 1, (x
1
∼ x
2
), (x
1
| x
2
)}
23.8. A = {x
1
| (x
3
∨ x
2
), x
3
→ (x
2
↓ x
1
), x
2
→ (x
1
∨ x
3
), (x
1
∼ x
2
)}
23.9. A = {x
2
∨ (x
2
→ x
1
), x
1
⊕ x
3
, x
1
x
2
, (x
1
⊕ x
3
) ↓ (x
1
∼ x
2
)}
23.10. A = {(x
2
∨ x
3
) ⊕ (x
3
∨ x
1
),
x
1
↓ (x
2
∨ x
3
), (x
3
∨ x
2
) ⊕ x
1
, x
1
| x
2
}
23.11. A = {(x
1
⊕ x
2
)(x
3
→ x
1
), x
1
∨ x
2
, x
1
x
2
, (x
3
∼ x
2
)(x
3
→ x
2
)}
23.12. A = {(x
3
↓ x
2
) → (x
1
⊕ x
3
), (x
2
→ x
3
) ∨ (x
1
→ x
2
), x
1
→ x
2
, x
1
⊕ x
2
}
23.13. A = {(x
2
∼ x
1
) ∨ x
2
, (x
2
∼ x
3
) | x
1
, x
3
∨ (x
2
⊕ x
3
), (x
1
∼ x
3
) ⊕ (x
1
x
2
)}
23.14. A = {(x
1
| x
2
) ↓ (x
1
↓ x
2
), (x
3
∨ x
2
)(x
2
→ x
1
), (x
1
∼ x
3
)(x
1
⊕ 1), x
1
x
2
}
23.15. A = {(x
1
x
2
)(x
2
→ x
1
), (x
1
x
2
) | x
3
, (x
2
| x
1
) → (x
2
| x
3
),
(x
1
↓ x
2
) ↓ x
2
}
23.16. A = {(x
3
→ x
2
) ∼ (x
2
→ x
1
), x
1
x
2
x
3
, x
1
⊕ x
2
, x
1
∨ x
2
}
23.17. A = {x
2
x
3
⊕ (x
1
| x
3
), x
2
↓ (x
2
→ x
1
), x
1
∼ x
2
∼ (x
2
→ x
1
),
x
2
x
3
(x
1
∨ x
3
)}
23.18. A = {(x
1
∨ x
2
) ∼ x
2
, (x
1
x
3
) → x
2
, (x
1
∼ x
3
) ⊕ x
2
, x
1
(x
3
→ x
2
)}
23.19. A = {(x
1
↓ x
3
) ⊕ x
2
, x
1
x
2
, (x
2
∼ x
1
) → x
1
, x
2
| (x
1
∨ x
3
)}
23.20. A = {(x
1
| x
2
) → x
3
, (x
1
→ x
2
), x
1
∼ x
2
, x
1
x
2
(x
1
→ x
3
)}
23.21. A = {x
1
→ (x
1
x
2
), (x
1
∼ x
2
) ⊕ x
2
, x
1
∼ (x
1
| x
2
), x
1
∼ x
2
}
23.22. A = {(x
1
x
3
) ↓ (x
1
↓ x
3
), (x
1
⊕ x
2
) ∼ (x
1
∨ x
2
), (x
1
∼ x
2
) ∨
x
2
,
(x
1
∨ x
2
) | (x
1
↓ x
2
)}
23.23. A = {(x
1
∼ x
2
), (x
1
∨ x
3
) ↓ (x
2
∼ x
3
), x
1
⊕ (x
1
↓ x
2
), (x
1
| x
2
) ↓ x
1
}
23.24. A = {x
1
∨ (x
2
→ x
1
), (x
1
x
2
) ∼ (x
2
x
3
), (x
1
⊕ x
3
) ∼ x
2
,
(x
2
⊕ x
1
) → (x
3
x
1
)}
23.25. A = {(x
2
∨ x
3
)(x
1
| x
3
), (x
2
→ x
1
) ∨ (x
3
→ x
1
), x
1
∨ (x
2
| x
3
),
(x
1
∼ x
3
)x
2
x
3
}
23.26. A = {x
1
∼ (x
3
→ x
2
), (x
1
| x
2
) | x
1
, x
1
↓ (x
2
↓ x
3
), x
1
∼ x
2
∼ x
3
}
25
23. Из системы функций выделить все базисы A.
 23.1. A = {x1 ∼ x2 , (x1 | x2 ) ⊕ (x3 ∨ x1 ), x2 ∼ (x3 ⊕ x1 ), x3 → (x1 ∼ x2 )}
 23.2. A = {x1 ∼ x2 , (x3 ⊕ x1 ) ↓ (x2 | x3 ), x1 ∨ x2 ∨ x3 , (x3 x2 ) ∨ (x2 ⊕ x3 )}
 23.3. A = {(x1 ↓ x3 ) ∨ x2 , (x3 ↓ x1 ) | (x2 → x1 ), x1 ∨ x2 ∨ (x3 | x1 ),
       (x1 | x2 ) ∨ (x2 ∼ x1 )}
 23.4. A = {x1 | (x2 → x1 ), (x2 x1 ) → x3 , x1 ⊕ x2 ⊕ x3 , (x3 → x2 ) ∼ (x1 ⊕ x2 )}
 23.5. A = {(x1 ∼ x2 ), (x1 ⊕ x2 ) ∨ x3 , (x1 | x2 )x1 , x1 → (x2 ∼ x3 )}
 23.6. A = {(x3 | x1 ) ∨ x2 ∨ x1 , x2 ⊕ (x1 ∨ x2 ), (x2 | x1 ) | x3 ,
       (x1 ↓ x3 ) ∨ (x2 → x3 )}
 23.7. A = {x3 (x1 ∼ x2 ), x1 ⊕ x2 ⊕ x3 ⊕ 1, (x1 ∼ x2 ), (x1 | x2 )}
 23.8. A = {x1 | (x3 ∨ x2 ), x3 → (x2 ↓ x1 ), x2 → (x1 ∨ x3 ), (x1 ∼ x2 )}
 23.9. A = {x2 ∨ (x2 → x1 ), x1 ⊕ x3 , x1 x2 , (x1 ⊕ x3 ) ↓ (x1 ∼ x2 )}
23.10. A = {(x2 ∨ x3 ) ⊕ (x3 ∨ x1 ), x1 ↓ (x2 ∨ x3 ), (x3 ∨ x2 ) ⊕ x1 , x1 | x2 }
23.11. A = {(x1 ⊕ x2 )(x3 → x1 ), x1 ∨ x2 , x1 x2 , (x3 ∼ x2 )(x3 → x2 )}
23.12. A = {(x3 ↓ x2 ) → (x1 ⊕ x3 ), (x2 → x3 ) ∨ (x1 → x2 ), x1 → x2 , x1 ⊕ x2 }
23.13. A = {(x2 ∼ x1 ) ∨ x2 , (x2 ∼ x3 ) | x1 , x3 ∨ (x2 ⊕ x3 ), (x1 ∼ x3 ) ⊕ (x1 x2 )}
23.14. A = {(x1 | x2 ) ↓ (x1 ↓ x2 ), (x3 ∨ x2 )(x2 → x1 ), (x1 ∼ x3 )(x1 ⊕ 1), x1 x2 }
23.15. A = {(x1 x2 )(x2 → x1 ), (x1 x2 ) | x3 , (x2 | x1 ) → (x2 | x3 ),
       (x1 ↓ x2 ) ↓ x2 }
23.16. A = {(x3 → x2 ) ∼ (x2 → x1 ), x1 x2 x3 , x1 ⊕ x2 , x1 ∨ x2 }
23.17. A = {x2 x3 ⊕ (x1 | x3 ), x2 ↓ (x2 → x1 ), x1 ∼ x2 ∼ (x2 → x1 ),
       x2 x3 (x1 ∨ x3 )}
23.18. A = {(x1 ∨ x2 ) ∼ x2 , (x1 x3 ) → x2 , (x1 ∼ x3 ) ⊕ x2 , x1 (x3 → x2 )}
23.19. A = {(x1 ↓ x3 ) ⊕ x2 , x1 x2 , (x2 ∼ x1 ) → x1 , x2 | (x1 ∨ x3 )}
23.20. A = {(x1 | x2 ) → x3 , (x1 → x2 ), x1 ∼ x2 , x1 x2 (x1 → x3 )}
23.21. A = {x1 → (x1 x2 ), (x1 ∼ x2 ) ⊕ x2 , x1 ∼ (x1 | x2 ), x1 ∼ x2 }
23.22. A = {(x1 x3 ) ↓ (x1 ↓ x3 ), (x1 ⊕ x2 ) ∼ (x1 ∨ x2 ), (x1 ∼ x2 ) ∨ x2 ,
       (x1 ∨ x2 ) | (x1 ↓ x2 )}
23.23. A = {(x1 ∼ x2 ), (x1 ∨ x3 ) ↓ (x2 ∼ x3 ), x1 ⊕ (x1 ↓ x2 ), (x1 | x2 ) ↓ x1 }
23.24. A = {x1 ∨ (x2 → x1 ), (x1 x2 ) ∼ (x2 x3 ), (x1 ⊕ x3 ) ∼ x2 ,
       (x2 ⊕ x1 ) → (x3 x1 )}
23.25. A = {(x2 ∨ x3 )(x1 | x3 ), (x2 → x1 ) ∨ (x3 → x1 ), x1 ∨ (x2 | x3 ),
       (x1 ∼ x3 )x2 x3 }
23.26. A = {x1 ∼ (x3 → x2 ), (x1 | x2 ) | x1 , x1 ↓ (x2 ↓ x3 ), x1 ∼ x2 ∼ x3 }

                                          25

Страницы