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\subsection{Binary functions}

\subsubsection{Properties of binary functions}

Binary functions can be written as:

\(f(a,b)=a\oplus b\)

A function is commutative if:

\(x\oplus y = y\oplus x\)

A function is associative if:

\((x\oplus y)\oplus z = x\oplus (y\oplus z)\)

A function \(\otimes \) is left distributive over \(\oplus \) if:

\(x\otimes (y\oplus z)=(x\otimes y) \oplus (x\otimes z)\)

Alternatively, function \(\otimes \) is right distributive over \(\oplus \) if:
\((x\oplus y)\otimes z=(x\otimes z) \oplus (y\oplus z)\)

A function is distributive over another function if it both left and right distributive over it.

