Implement a Boolean function using an 8x1 deMUX
Maybe everyone's over thinking this (or I'm missing something).

I don't think you need the logic going into D, just tie D to 1.  Then, route M1, M3, and M5 into the OR gate whose output is F.  The output will be 1 for just the correct entries of x,y and z, and 0 otherwise (i.e. 111 will have a 0 output since M7 is not fed into the OR gate).

So that's how to do it with one OR gate.  Not sure about AND ...