Rules of Boolean Algebra

Question	Answer
A $\cdot$ 1 =	A
A $\cdot$ 0 =	0
A + 1 =	1
A + 0 =	A
Zero and Unit Rules.	A + 0 = A, A + 1 = 1, A $\cdot$ 0 = 0, A $\cdot$ 1 = A
A $\cdot$ $\bar A$ =	0
A + $\bar A$ =	1
$\overline {(\bar A)}$ =	A
Complement Relations	$\overline {(\bar A)}$ = A, A + $\bar A$ = 1, A $\cdot$ $\bar A$ = 0
A $\cdot$ A =	A
A + A =	A
Idempotence	A $\cdot$ A = A, A + A = A
A $\cdot$ B =	B $\cdot$ A
A + B =	B + A
Commutative Laws	A $\cdot$ B = B $\cdot$ A, A + B = B + A
A + (A $\cdot$ B) =	A
A $\cdot$ (A + B) =	A
A + ( $\bar A$ $\cdot$ B) =	A + B
Absorption Laws	A + ( $\bar A$ $\cdot$ B) = A + B, A $\cdot$ (A + B) = A, A + (A $\cdot$ B) = A
A $\cdot$ (B + C) =	(A $\cdot$ B) + (A $\cdot$ C)
A + (B $\cdot$ C) =	(A + B) $\cdot$ (A + C)
Distributive Laws	A $\cdot$ (B + C) = (A $\cdot$ B) + (A $\cdot$ C), A + (B $\cdot$ C) = (A + B) $\cdot$ (A + C)
A + B + C =	A + (B + C) = (A + B) + C
A $\cdot$ B $\cdot$ C =	A $\cdot$ (B $\cdot$ C) = (A $\cdot$ B) $\cdot$ C
Associative Laws	A $\cdot$ B $\cdot$ C = A $\cdot$ (B $\cdot$ C), A + B + C = A + (B + C)
$\overline {A + B + C}$ =	$\bar A$ $\cdot$ $\bar B$ $\cdot$ $\bar C$
$\overline {A \cdot\ B \cdot\ C}$ =	$\bar A$ + $\bar B$ + $\bar C$
De Morgan's Theorem	$\overline {A + B + C}$ = $\bar A$ $\cdot$ $\bar B$ $\cdot$ $\bar C$ , $\overline {A \cdot\ B \cdot\ C}$ = $\bar A$ + $\bar B$ + $\bar C$

Resource summary

	Created by cameronfdowner over 9 years ago