Промежуточные таблицы истинности:X∧Y:
(X∧Y)∧Z:
X | Y | Z | X∧Y | (X∧Y)∧Z |
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 |
¬Y:
¬Z:
X∧(¬Y):
X | Y | ¬Y | X∧(¬Y) |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
(X∧(¬Y))∧(¬Z):
X | Y | Z | ¬Y | X∧(¬Y) | ¬Z | (X∧(¬Y))∧(¬Z) |
0 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 | 0 | 0 |
(X∧Y)∧V:
X | Y | V | X∧Y | (X∧Y)∧V |
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 |
¬X:
(¬X)∧(¬Y):
X | Y | ¬X | ¬Y | (¬X)∧(¬Y) |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
((¬X)∧(¬Y))∧Z:
X | Y | Z | ¬X | ¬Y | (¬X)∧(¬Y) | ((¬X)∧(¬Y))∧Z |
0 | 0 | 0 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 0 | 0 |
(((¬X)∧(¬Y))∧Z)∧V:
X | Y | Z | V | ¬X | ¬Y | (¬X)∧(¬Y) | ((¬X)∧(¬Y))∧Z | (((¬X)∧(¬Y))∧Z)∧V |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
¬((X∧Y)∧Z):
X | Y | Z | X∧Y | (X∧Y)∧Z | ¬((X∧Y)∧Z) |
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 |
¬((X∧(¬Y))∧(¬Z)):
X | Y | Z | ¬Y | X∧(¬Y) | ¬Z | (X∧(¬Y))∧(¬Z) | ¬((X∧(¬Y))∧(¬Z)) |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |
¬((X∧Y)∧V):
X | Y | V | X∧Y | (X∧Y)∧V | ¬((X∧Y)∧V) |
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 |
¬((((¬X)∧(¬Y))∧Z)∧V):
X | Y | Z | V | ¬X | ¬Y | (¬X)∧(¬Y) | ((¬X)∧(¬Y))∧Z | (((¬X)∧(¬Y))∧Z)∧V | ¬((((¬X)∧(¬Y))∧Z)∧V) |
0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
(¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))):
X | Y | Z | X∧Y | (X∧Y)∧Z | ¬((X∧Y)∧Z) | ¬Y | X∧(¬Y) | ¬Z | (X∧(¬Y))∧(¬Z) | ¬((X∧(¬Y))∧(¬Z)) | (¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))) |
0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)):
X | Y | Z | V | X∧Y | (X∧Y)∧Z | ¬((X∧Y)∧Z) | ¬Y | X∧(¬Y) | ¬Z | (X∧(¬Y))∧(¬Z) | ¬((X∧(¬Y))∧(¬Z)) | (¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))) | X∧Y | (X∧Y)∧V | ¬((X∧Y)∧V) | ((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
(((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)))∧(¬((((¬X)∧(¬Y))∧Z)∧V)):
X | Y | Z | V | X∧Y | (X∧Y)∧Z | ¬((X∧Y)∧Z) | ¬Y | X∧(¬Y) | ¬Z | (X∧(¬Y))∧(¬Z) | ¬((X∧(¬Y))∧(¬Z)) | (¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))) | X∧Y | (X∧Y)∧V | ¬((X∧Y)∧V) | ((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)) | ¬X | ¬Y | (¬X)∧(¬Y) | ((¬X)∧(¬Y))∧Z | (((¬X)∧(¬Y))∧Z)∧V | ¬((((¬X)∧(¬Y))∧Z)∧V) | (((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)))∧(¬((((¬X)∧(¬Y))∧Z)∧V)) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
¬((((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)))∧(¬((((¬X)∧(¬Y))∧Z)∧V))):
X | Y | Z | V | X∧Y | (X∧Y)∧Z | ¬((X∧Y)∧Z) | ¬Y | X∧(¬Y) | ¬Z | (X∧(¬Y))∧(¬Z) | ¬((X∧(¬Y))∧(¬Z)) | (¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))) | X∧Y | (X∧Y)∧V | ¬((X∧Y)∧V) | ((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)) | ¬X | ¬Y | (¬X)∧(¬Y) | ((¬X)∧(¬Y))∧Z | (((¬X)∧(¬Y))∧Z)∧V | ¬((((¬X)∧(¬Y))∧Z)∧V) | (((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)))∧(¬((((¬X)∧(¬Y))∧Z)∧V)) | ¬((((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)))∧(¬((((¬X)∧(¬Y))∧Z)∧V))) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
Общая таблица истинности:
X | Y | Z | V | X∧Y | (X∧Y)∧Z | ¬Y | ¬Z | X∧(¬Y) | (X∧(¬Y))∧(¬Z) | (X∧Y)∧V | ¬X | (¬X)∧(¬Y) | ((¬X)∧(¬Y))∧Z | (((¬X)∧(¬Y))∧Z)∧V | ¬((X∧Y)∧Z) | ¬((X∧(¬Y))∧(¬Z)) | ¬((X∧Y)∧V) | ¬((((¬X)∧(¬Y))∧Z)∧V) | (¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))) | ((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)) | (((¬((X∧Y)∧Z))∧(¬((X∧(¬Y))∧(¬Z))))∧(¬((X∧Y)∧V)))∧(¬((((¬X)∧(¬Y))∧Z)∧V)) | ¬(¬(X∧Y∧Z)∧¬(X∧¬Y∧¬Z)∧¬(X∧Y∧V)∧¬(¬X∧¬Y∧Z∧V)) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности:
X | Y | Z | V | F |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
F
сднф = ¬X∧¬Y∧Z∧V ∨ X∧¬Y∧¬Z∧¬V ∨ X∧¬Y∧¬Z∧V ∨ X∧Y∧¬Z∧V ∨ X∧Y∧Z∧¬V ∨ X∧Y∧Z∧V
Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности:
X | Y | Z | V | F |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
F
скнф = (X∨Y∨Z∨V) ∧ (X∨Y∨Z∨¬V) ∧ (X∨Y∨¬Z∨V) ∧ (X∨¬Y∨Z∨V) ∧ (X∨¬Y∨Z∨¬V) ∧ (X∨¬Y∨¬Z∨V) ∧ (X∨¬Y∨¬Z∨¬V) ∧ (¬X∨Y∨¬Z∨V) ∧ (¬X∨Y∨¬Z∨¬V) ∧ (¬X∨¬Y∨Z∨V)
Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции
X | Y | Z | V | Fж |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
Построим полином Жегалкина:
F
ж = C
0000 ⊕ C
1000∧X ⊕ C
0100∧Y ⊕ C
0010∧Z ⊕ C
0001∧V ⊕ C
1100∧X∧Y ⊕ C
1010∧X∧Z ⊕ C
1001∧X∧V ⊕ C
0110∧Y∧Z ⊕ C
0101∧Y∧V ⊕ C
0011∧Z∧V ⊕ C
1110∧X∧Y∧Z ⊕ C
1101∧X∧Y∧V ⊕ C
1011∧X∧Z∧V ⊕ C
0111∧Y∧Z∧V ⊕ C
1111∧X∧Y∧Z∧V
Так как F
ж(0000) = 0, то С
0000 = 0.
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 = 0 ⊕ 1 = 1
F
ж(0100) = С
0000 ⊕ С
0100 = 0 => С
0100 = 0 ⊕ 0 = 0
F
ж(0010) = С
0000 ⊕ С
0010 = 0 => С
0010 = 0 ⊕ 0 = 0
F
ж(0001) = С
0000 ⊕ С
0001 = 0 => С
0001 = 0 ⊕ 0 = 0
F
ж(1100) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
1100 = 0 => С
1100 = 0 ⊕ 1 ⊕ 0 ⊕ 0 = 1
F
ж(1010) = С
0000 ⊕ С
1000 ⊕ С
0010 ⊕ С
1010 = 0 => С
1010 = 0 ⊕ 1 ⊕ 0 ⊕ 0 = 1
F
ж(1001) = С
0000 ⊕ С
1000 ⊕ С
0001 ⊕ С
1001 = 1 => С
1001 = 0 ⊕ 1 ⊕ 0 ⊕ 1 = 0
F
ж(0110) = С
0000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0110 = 0 => С
0110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(0101) = С
0000 ⊕ С
0100 ⊕ С
0001 ⊕ С
0101 = 0 => С
0101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(0011) = С
0000 ⊕ С
0010 ⊕ С
0001 ⊕ С
0011 = 1 => С
0011 = 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(1110) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
0010 ⊕ С
1100 ⊕ С
1010 ⊕ С
0110 ⊕ С
1110 = 1 => С
1110 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 0
F
ж(1101) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
0001 ⊕ С
1100 ⊕ С
1001 ⊕ С
0101 ⊕ С
1101 = 1 => С
1101 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(1011) = С
0000 ⊕ С
1000 ⊕ С
0010 ⊕ С
0001 ⊕ С
1010 ⊕ С
1001 ⊕ С
0011 ⊕ С
1011 = 0 => С
1011 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 = 1
F
ж(0111) = С
0000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0001 ⊕ С
0110 ⊕ С
0101 ⊕ С
0011 ⊕ С
0111 = 0 => С
0111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 1
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 = 1 => С
1111 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 = 0
Таким образом, полином Жегалкина будет равен:
F
ж = X ⊕ X∧Y ⊕ X∧Z ⊕ Z∧V ⊕ X∧Y∧V ⊕ X∧Z∧V ⊕ Y∧Z∧V
Логическая схема, соответствующая полиному Жегалкина: