I'm supposed to give the other interpretation for this question, but I don't even understand how it can be ambiguous. Please help.
Domain: Frances et al.
P(x) x is a pianist.
W(x,y) x works for y.
F(x,y,z) x is friendlier to y than to z
A(x) x is an artist.
L(x,y) x is more lazy than y.
M(x) x is a master sewer.
T(x) x has a ptarmigan.
m Mackenzie
j Jilly-Joe
Using the key given, symbolize the following sentences in FOL.
The natural interpretation of "Every artist works for someone that all pianists works for" is probably that there is one boss (probably Anouk!) that employs all pianists, and all artists work for her. Formalize the other reading.
The sentence places no restriction on the size of $S$, where for every person $s\in S$, we have that all pianists work for $s$.
So to satisfy the sentence, we just have to have each artist work for some $s\in S$. In particular, there need not be one person $p$ such that all pianists work for $p$, and that all artists work for $p$.
(Note: I could have used the word "employed" to avoid using set notation, but I just want to be precise here)