Answer:
a) ∀x ∃f F(x, f)
b) ∃e ∀y F(e, y)
c) ∀x ∃y F(x, y)
d) ¬∃x ∀y F(x, y) ≡ ∃x ∀y ¬F(x, y)
e) ∃x ∃y F(x, y)
f) ¬∃x ∃f ∃j [F(x, f) ∧ F(x, j)] ≡ ∃x ∃f ∃j ¬[F(x, f) ∧ F(x, j)]
g) ∃n ∃a ∃b [F(n, a) ∧ F(n, b)]
Step-by-step explanation: F (x, y) "x can fool y,"
domain consists of all people in the world
a) Everybody can fool Fred.
Let's say Fred = f ∈ y
∀x ∃f F(x, f)
b) Evelyn can fool everybody.
Let's say Evelyn = e ∈ x
∃e ∀y F(e, y)
c) Everybody can fool somebody.
∀x ∃y F(x, y)
d) There is no one who can fool everybody.
¬∃x ∀y F(x, y) ≡ ∃x ∀y ¬F(x, y)
e) Everyone can be fooled by somebody.
∃x ∃y F(x, y)
f) No one can fool both Fred and Jerry.
Let's say Fred = f ∈ y
Let's say Jerry = j ∈ y
¬∃x ∃f ∃j [F(x, f) ∧ F(x, j)] ≡ ∃x ∃f ∃j ¬[F(x, f) ∧ F(x, j)]
g) Nancy can fool exactly two people.
Let's say Nancy = n ∈ x
Let's say person 1 = a ∈ y
Let's say person 2 = b ∈ y
∃n ∃a ∃b [F(n, a) ∧ F(n, b)]
