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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

\(0 \neq 1\)