French Classical Sauces

Escoffier may list hundreds but there are only 23.

W
O
W/S
O/W
S/W
(O + S)/W
(W/S)/W
O + (W/S)
(G + O)/W
(G + O + S)/W
(O + (W/S))/W
(S + (W/S))/W
((W + S)/O)/S
(O + S + (W/S))/W
((W/S) + (S ⊂ W))/W
(O + (W/S)/W)/S
((O + (W/S))/W)/S
(O/W) + ((G + O)/W)
(O + (W/S) + (S ⊂ W))/W
(S + (W/S) + (S ⊂ W))/W
(((W/S) + (S ⊂ W))/W)/S
(O + S +(W/S) + (S ⊂ W))/W
(O + S +((G + O)/W))/W

Key (letters): O = oil, W = water, G = gas, S = solid
Key (operators): + = mixed into, / = dispersed into, ⊂ = included into

For example, both broth or vinegar are just W, and butter is (W/O)/S.

Note that in a given formula, the multiple W's and S'es may be different.

This is the work of the magnificent Hervé This, co-inventor of the field of molecular gastronomy.

See if you can come up with examples of the above sauces, fellow gastronauts!