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# Huntington's postulates

Huntingtonâ€™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

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

## Distinct elements

$$0 \neq 1$$
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