Demultiplexer Equation?

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I am currently working on a project that requires a demultiplexer to be used. My problem is that I want to represent it in equation form, but no matter how much I try I cannot find the equation for a demultiplexer! I have tried to come up with a equation, but I only know how to Veitch diagram, and Karnaugh maps are getting me nowhere as I have never understood them. If the equation for a demultiplexer could be provided, or someone could teach me how to get the equation for it, then that would be great!

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Multiplexor: If the inputs are $A,B$ and the select line is $S$, then the output is $O=\bar{S}A+S B$. When $S$ is false, $A$ is selected, when $S$ is true, $B$ is selected.

Demultiplexor: Suppose the input is $I$, and the deselect line is $D$, then you will have two outputs, $O_0 = \bar{D} I$, and $O_1 = D I$.