|
0 + X = X
|
|
0 · X = 0
|
|
1 + X = 1
|
|
1 · X = X
|
|
X + X = X
|
|
X · X = X
|
|
X + ~X = 1
|
|
~0 = 1
|
|
~1 = 0
|
|
~~X = X
|
|
X · ~X = 0
|
|
Communative Law
|
A · B = B · A
|
|
A + B = B + A
|
|
|
Associative Law
|
A · (B · C) = (A · B) · C
|
|
A + (B + C) = (A + B) +C
|
|
|
Distributive Law
|
A · (B + C) = A·B + A·C
|
|
A + B · C = (A+B)(A+C)
|
|
~(X · Y)
|
= X + Y
|
|
~(X + Y)
|
= X · Y
|
|
~(X · Y · Z)
|
= X + Y + ~Z
|
|
~(X + Y + Z)
|
= X · Y · ~Z
|
|
Theorem 1
X + X · Y = X
|
|
Theorem 2
X + ~X · Y = X + Y
|
|
Theorem 3
X · Y + X · Z + Y · Z = X · Y + X · Z
|
|
Theorem 4
X(X + Y) = X
|
|
Theorem 5
X(~X + Y) = X · Y
|
|
Theorem 6
(X + Y)(X + ~Y) = X
|
|
Theorem 7
(X + Y)(X + Z) = X · Z + X · Y
|
|
Theorem 8
(X + Y)(X + Z)(Y + Z) = (X + Y)(X + Z)
|
Cheatography n. The art of mapping complex subjects into clear, instantly navigable reference guides.
