EDB — 1WF

[1WF](Proposed on 2022-12) Consider the sets:

• \(P\) all the professors,

• \(S\) all scientists,

• \(F\) the set of philosophers,

• \(M\) the set of mathematicians.

For each of the following sentences, write a formula that represents it, using the above sets, the empty set, relations \(⊆,=,≠\), and set operations \(∪,∩,⧵\).

• not all professors are scientists

• some mathematician is philosopher;

• if a philosopher is not a mathematician then s/he is a professor;

• all philosophers are scientists or professors, but not mathematicians;

• if there is a mathematician who is also a scientist, then s/he is neither a philosopher nor a professor.