Answer:
See steps below
Step-by-step explanation:
Let F(x, y) and W be
F(x,y) = “x can fool y”
W the set of all the people in the world
a) Everybody can fool Fred.
[tex]\forall x \in W,F(x, Fred)[/tex]
b) Evelyn can fool everybody.
[tex]\forall y\in W, F(Evelyn, y)[/tex]
c) Everybody can fool somebody.
[tex]\forall x \in W,\exists y :F(x,y)[/tex]
d) There is no one who can fool everybody.
[tex]\nexists x \in W: \forall y ,F(x,y)[/tex]
e) No one can fool both Fred and Jennifer.
[tex]\nexists x \in W: F(x,Fred)\wedge F(x,Jennifer)[/tex]
f) Nancy can fool exactly two people.
[tex]\exists x,y \in W:\forall z\neq x,z\neq y, F(Nancy,x)\wedge F(Nancy,y)\wedge (\neg F(Nancy,z))[/tex]
