Boolean Identities

The identities below are the same as on the previous slide but use the operations: $'$, $\cdot$, and $+$ instead of: $\neg$, $\wedge$, and $\vee$:

Name	Conjunction ($\cdot$) version	Disjunction ($+$) version
Identity Law	$1x = x$	$0 + x = x$
Null Law	$0x = 0$	$1 + x = 1$
Idempotent Law	$xx = x$	$x + x = x$
Complement Law	$xx' = 0$	$x + x' = 1$
Commutative Law	$xy = yx$	$x + y = y + x$
Associative Law	$(xy)z = x(yz)$	$(x + y) + z = x + (y + z)$
Distributive Law	$x + yz = (x + y)(x + z)$	$x(y + z) = xy + xz$
Absorption Law	$x(x + y) = x$	$x + xy = x$
DeMorgan's Law	$(xy)' = x' + y'$	$(x + y)' = x'y'$
Double Negation Law	$(x')'= x'' = x$