This doesn't capture the case where:
the chemist mole and the zoologist mole and the government mole are all valid, but the dermatologist one isn't
Or the case where
the chemist mole and the zoologist mole and the dermatologist mole are all valid, but the government one isn'tthe chemist mole and the government mole and the dermatologist mole are all valid, but the zoologist one isn'tthe government mole and the zoologist mole and the dermatologist mole are all valid, but the chemist one isn't
If you make a Venn Diagram from circles, for every circle above 3 you need to increase the number of dimensions of the circles AND the domain-space (the paper it is drawn on) by 1.