Intro to Logic Questions Using the symbolization key given below, symbolize each English sentence in FOL (First-Order Logic).

Here is the key for inputting the logical connectives and quantifiers into Carnap:

type ~ or "not" for negation
type \/ or "or" for disjunction
type /\ or "and" for conjunction
type > or -> for conditional
type <> or <-> for biconditional
type Ax for the universal quantifier
type Ex for the existential quantifier
Here is the symbolization key:

Domain: people
C(x) = x knows the combination to the safe.
S(x) = x is a spy.
V(x) = x is a vegetarian.
h = Hofthor
g = Galadriel

1.No one knows the combination to the safe unless everyone is either a spy or vegetarian.

2.Every spy who knows the combination to the safe is a vegetarian if, and only if, either Hofthor is not a spy or Hofthor does not know the combination to the safe.

3.Every vegetarian knows the combination to the safe only if some spy who knows the combination to the safe is also a vegetarian.