Postulates, Properties, and Theorems of Boolean Algebra (1450)

X + 0 = ?

X

X + 1 = ?

1

X + X = ?

X

X + X^’ = ?

1

X ^. 0 = ?

0

X ^. 1 = ?

X

X ^. X = ?

X

X ^. X^’ = ?

0

Involution Property 1: X^{’ ’} = ?

X^{’ ’} = X

Commutative Property 1: X + Y = ?

X + Y = Y + X

Commutative Property 2: X ^. Y = ?

X ^. Y = Y ^. X

Associative Property 1: X + (Y + Z) = ?

X + (Y + Z) = (X + Y) + Z

Associative Property 2: X ^. (Y ^. Z) = ?

X ^. (Y ^. Z) = (X ^. Y) ^. Z

Absorption Property 1: X + X ^. Y = ?

X + X ^. Y = X

Absorption Property 2: X ^. (X + Y) = ?

X ^. (X + Y) = X

Distributive Property 1: X ^. (Y + Z) = ?

X ^. (Y + Z) = XY + XZ

Distributive Property 2: X + YZ = ?

X + YZ = (X + Y) ^. (X + Z)

DeMorgan’s Theorem 1: (X + Y)^’ = ?

(X + Y)^’ = X^{’ .} Y^’

DeMorgan’s Theorem 2: (X ^. Y)^’ = ?

(X ^. Y)^’ = X^’ + Y^’