Is demultiplexer universal gate?
Formally, the demultiplexer is not universal (functionally complete) because it is falsity-preserving -- that is, if you set all the inputs to 0, you can't get a 1 out of any combination of demuxes.

(Note that a demux actually calculates two functions, and would therefore be considered two "gates" in abstract logic: the AND gate and a does-not-imply gate. Both these gates have the falsity-preserving characteristic, so the set containing both of them is not universal either.)

You can make a universal set by including the constant 1 -- this is easy to do in real electronics, where you may just tie an input to +Vcc. In other words, the set consisting of {AND, does-not-imply, 1} is universal.