Промежуточные таблицы истинности:¬X4:
X2∧X3:
(X2∧X3)∧(¬X4):
X2 | X3 | X4 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) |
0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 0 |
¬((X2∧X3)∧(¬X4)):
X2 | X3 | X4 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) |
0 | 0 | 0 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 | 0 |
1 | 1 | 1 | 1 | 0 | 0 | 1 |
¬X1:
(¬X1)∧(¬((X2∧X3)∧(¬X4))):
X1 | X2 | X3 | X4 | ¬X1 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) | (¬X1)∧(¬((X2∧X3)∧(¬X4))) |
0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
¬((¬X1)∧(¬((X2∧X3)∧(¬X4)))):
X1 | X2 | X3 | X4 | ¬X1 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) | (¬X1)∧(¬((X2∧X3)∧(¬X4))) | ¬((¬X1)∧(¬((X2∧X3)∧(¬X4)))) |
0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
(X2∧X3)∧X4:
X2 | X3 | X4 | X2∧X3 | (X2∧X3)∧X4 |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 |
¬((X2∧X3)∧X4):
X2 | X3 | X4 | X2∧X3 | (X2∧X3)∧X4 | ¬((X2∧X3)∧X4) |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 0 | 0 | 1 |
1 | 0 | 0 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 0 |
¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))):
X1 | X2 | X3 | X4 | ¬X1 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) | (¬X1)∧(¬((X2∧X3)∧(¬X4))) | ¬((¬X1)∧(¬((X2∧X3)∧(¬X4)))) | ¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))) |
0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
(¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))))∨X:
X1 | X2 | X3 | X4 | X | ¬X1 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) | (¬X1)∧(¬((X2∧X3)∧(¬X4))) | ¬((¬X1)∧(¬((X2∧X3)∧(¬X4)))) | ¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))) | (¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))))∨X |
0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
¬(¬X1):
(¬(¬X1))∧(X2∧X3):
X1 | X2 | X3 | ¬X1 | ¬(¬X1) | X2∧X3 | (¬(¬X1))∧(X2∧X3) |
0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 1 |
¬((¬(¬X1))∧(X2∧X3)):
X1 | X2 | X3 | ¬X1 | ¬(¬X1) | X2∧X3 | (¬(¬X1))∧(X2∧X3) | ¬((¬(¬X1))∧(X2∧X3)) |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 |
(¬((¬(¬X1))∧(X2∧X3)))∧(¬X4):
X1 | X2 | X3 | X4 | ¬X1 | ¬(¬X1) | X2∧X3 | (¬(¬X1))∧(X2∧X3) | ¬((¬(¬X1))∧(X2∧X3)) | ¬X4 | (¬((¬(¬X1))∧(X2∧X3)))∧(¬X4) |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
((¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))))∨X)∨((¬((¬(¬X1))∧(X2∧X3)))∧(¬X4)):
X1 | X2 | X3 | X4 | X | ¬X1 | X2∧X3 | ¬X4 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) | (¬X1)∧(¬((X2∧X3)∧(¬X4))) | ¬((¬X1)∧(¬((X2∧X3)∧(¬X4)))) | ¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))) | (¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))))∨X | ¬X1 | ¬(¬X1) | X2∧X3 | (¬(¬X1))∧(X2∧X3) | ¬((¬(¬X1))∧(X2∧X3)) | ¬X4 | (¬((¬(¬X1))∧(X2∧X3)))∧(¬X4) | ((¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))))∨X)∨((¬((¬(¬X1))∧(X2∧X3)))∧(¬X4)) |
0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
Общая таблица истинности:
X1 | X2 | X3 | X4 | ¬X4 | X2∧X3 | (X2∧X3)∧(¬X4) | ¬((X2∧X3)∧(¬X4)) | ¬X1 | (¬X1)∧(¬((X2∧X3)∧(¬X4))) | ¬((¬X1)∧(¬((X2∧X3)∧(¬X4)))) | (X2∧X3)∧X4 | ¬((X2∧X3)∧X4) | ¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))) | (¬(¬((¬X1)∧(¬((X2∧X3)∧(¬X4))))))∨X | ¬(¬X1) | (¬(¬X1))∧(X2∧X3) | ¬((¬(¬X1))∧(X2∧X3)) | (¬((¬(¬X1))∧(X2∧X3)))∧(¬X4) | (¬(¬(¬X1∧(¬(X2∧X3∧(¬X4)))))∨(X1¬(X2∧X3∧X4)))∨((¬(¬(¬X1)∧(X2∧X3))∧(¬X4))) |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности:
X1 | X2 | X3 | X4 | F |
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
F
сднф = ¬X1∧¬X2∧¬X3∧¬X4 ∨ ¬X1∧¬X2∧¬X3∧X4 ∨ ¬X1∧¬X2∧X3∧¬X4 ∨ ¬X1∧¬X2∧X3∧X4 ∨ ¬X1∧X2∧¬X3∧¬X4 ∨ ¬X1∧X2∧¬X3∧X4 ∨ ¬X1∧X2∧X3∧¬X4 ∨ ¬X1∧X2∧X3∧X4 ∨ X1∧¬X2∧¬X3∧¬X4 ∨ X1∧¬X2∧X3∧¬X4 ∨ X1∧X2∧¬X3∧¬X4
Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности:
X1 | X2 | X3 | X4 | F |
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
F
скнф = (¬X1∨X2∨X3∨¬X4) ∧ (¬X1∨X2∨¬X3∨¬X4) ∧ (¬X1∨¬X2∨X3∨¬X4) ∧ (¬X1∨¬X2∨¬X3∨X4) ∧ (¬X1∨¬X2∨¬X3∨¬X4)
Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции
X1 | X2 | X3 | X4 | Fж |
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
Построим полином Жегалкина:
F
ж = C
0000 ⊕ C
1000∧X1 ⊕ C
0100∧X2 ⊕ C
0010∧X3 ⊕ C
0001∧X4 ⊕ C
1100∧X1∧X2 ⊕ C
1010∧X1∧X3 ⊕ C
1001∧X1∧X4 ⊕ C
0110∧X2∧X3 ⊕ C
0101∧X2∧X4 ⊕ C
0011∧X3∧X4 ⊕ C
1110∧X1∧X2∧X3 ⊕ C
1101∧X1∧X2∧X4 ⊕ C
1011∧X1∧X3∧X4 ⊕ C
0111∧X2∧X3∧X4 ⊕ C
1111∧X1∧X2∧X3∧X4
Так как F
ж(0000) = 1, то С
0000 = 1.
Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы:
F
ж(1000) = С
0000 ⊕ С
1000 = 1 => С
1000 = 1 ⊕ 1 = 0
F
ж(0100) = С
0000 ⊕ С
0100 = 1 => С
0100 = 1 ⊕ 1 = 0
F
ж(0010) = С
0000 ⊕ С
0010 = 1 => С
0010 = 1 ⊕ 1 = 0
F
ж(0001) = С
0000 ⊕ С
0001 = 1 => С
0001 = 1 ⊕ 1 = 0
F
ж(1100) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
1100 = 1 => С
1100 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(1010) = С
0000 ⊕ С
1000 ⊕ С
0010 ⊕ С
1010 = 1 => С
1010 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(1001) = С
0000 ⊕ С
1000 ⊕ С
0001 ⊕ С
1001 = 0 => С
1001 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
F
ж(0110) = С
0000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0110 = 1 => С
0110 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(0101) = С
0000 ⊕ С
0100 ⊕ С
0001 ⊕ С
0101 = 1 => С
0101 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(0011) = С
0000 ⊕ С
0010 ⊕ С
0001 ⊕ С
0011 = 1 => С
0011 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(1110) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
0010 ⊕ С
1100 ⊕ С
1010 ⊕ С
0110 ⊕ С
1110 = 0 => С
1110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 1
F
ж(1101) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
0001 ⊕ С
1100 ⊕ С
1001 ⊕ С
0101 ⊕ С
1101 = 0 => С
1101 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(1011) = С
0000 ⊕ С
1000 ⊕ С
0010 ⊕ С
0001 ⊕ С
1010 ⊕ С
1001 ⊕ С
0011 ⊕ С
1011 = 0 => С
1011 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(0111) = С
0000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0001 ⊕ С
0110 ⊕ С
0101 ⊕ С
0011 ⊕ С
0111 = 1 => С
0111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(1111) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0001 ⊕ С
1100 ⊕ С
1010 ⊕ С
1001 ⊕ С
0110 ⊕ С
0101 ⊕ С
0011 ⊕ С
1110 ⊕ С
1101 ⊕ С
1011 ⊕ С
0111 ⊕ С
1111 = 0 => С
1111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 1
Таким образом, полином Жегалкина будет равен:
F
ж = 1 ⊕ X1∧X4 ⊕ X1∧X2∧X3 ⊕ X1∧X2∧X3∧X4
Логическая схема, соответствующая полиному Жегалкина: