Huntington's postulates

Huntington’s postulates define 6 axioms that any Boolean algebra must satisfy.

Closure

The result of a logical operation belongs to the set $\{0,1\}$.

Identity

$x+0=x$ and $x\cdot 1=x$

Commutativity

$x+y=y+x$ and $x\cdot y=y\cdot x$

Distributivity

$x(y+z)=(x\cdot y)+(x\cdot z)$ and $x+(y\cdot z)=(x+y)\cdot (x+z)$

Complements

$x+x^{\prime }=1$ and $x\cdot x^{\prime }=0$

Distinct elements

$0\ne 1$