Answer
a) A(Louis, Professor Michaels)
b) ∀x(S(x)->A(x, Professor Gross)
c) ∀x(F(x)->(A(x, Professor Miller) V A(Professor Miller, x)))
d) ∃x∀y(S(x)^F(y)->¬A(x,y))
e) ∃x∃y(S(x)^F(y)->¬A(x,y))
f) ∃x∀y(S(x)^F(y)->A(x,y))
g) ∃x∀y((F(x)^F(y)->A(x,y))
h) ∃x∃y(F(x)^S(y)->¬A(x,y))
Work Step by Step
a) A(Louis, Professor Michaels)
b) ∀x(S(x)->A(x, Professor Gross)
c) ∀x(F(x)->(A(x, Professor Miller) V A(Professor Miller, x)))
d) ∃x∀y(S(x)^F(y)->¬A(x,y))
e) ∃x∃y(S(x)^F(y)->¬A(x,y))
f) ∃x∀y(S(x)^F(y)->A(x,y))
g) ∃x∀y((F(x)^F(y)->A(x,y))
h) ∃x∃y(F(x)^S(y)->¬A(x,y))
