Boolean laws

De Morgan’s Laws

Expanding or factorising out negations

One negation of the whole operator becomes two negated literals with a changed operator

Distributive law

X and (Y or Z) = (X and Y) or (X and Z)

X or (Y and Z) = (X or Y) and (X or Z)

Associative law

Adding or removing brackets and reordering literals.

(So the pointless stuff really)

Commutative law

The order of which literals are presented around an operator does not matter.

e.g. A or B = B or A

Double negation

Double negations can simply be removed

Absorption

X or (X and Y) = X

X and (X or Y) = X

NAND

Only returns false when both inputs are true