Nice try, Andy, but logic failure. :p A musician isn't a number, so can't be reduced to an equation. A musician is a label i.e. a class or set item. Not an equation, but a Venn diagram (for which there is actually notation; but it's notation not an equation).

Musician & non-musician are sets that do not overlap.

Singer is a set within musician, as is instrumentalist.

Singer & instrumentalist may or may not overlap, but both must lie (through their back teeth, if you've met some of the ones I have; they're as bad as fishermen!) wholly within musician.

Therefore, regardless of bathroom or opera house, they can never overlap non-musician.

So there! ;-)