select the best translation into predicate logic, using the following translation key:
a: one
b: two
c: three
f(x): the successor of x
g(x,y): the sum of x and y
Nx: x is a number
Dxy: x is divisible by y
Gxy: x is greater than y
-Any number is divisible by two if, and only if, the successor of its successor is divisible by two.
A) (∀x)[Nx ⊃ Df(f(b))c]
B) (∀x){Nx ≡ [Dxb • Df(f(x))b]}
C) (∀x){Nx ⊃ [Dbx ≡ Df(x)b]}
D) (∀x){(Nx ⊃ Dxb) ≡ Df(f(x))b}
E) (∀x){Nx ⊃ [Dxb ≡ Df(f(x))b}

Question

select the best translation into predicate logic, using the following translation key: 
a: one
b: two 
c: three
f(x): the successor of x 
g(x,y): the sum of x and y 
Nx: x is a number
Dxy: x is divisible by y 
Gxy: x is greater than y
-Any number is divisible by two if, and only if, the successor of its successor is divisible by two.
A) (∀x)[Nx ⊃ Df(f(b))c]
B) (∀x){Nx ≡ [Dxb • Df(f(x))b]}
C) (∀x){Nx ⊃ [Dbx ≡ Df(x)b]}
D) (∀x){(Nx ⊃ Dxb) ≡ Df(f(x))b}
E) (∀x){Nx ⊃ [Dxb ≡ Df(f(x))b}

Quizplus · Accepted Answer

The correct translation is "Any number is divisible by two if, and only if, the successor of its successor is divisible by two." This is represented by E) (∀x){Nx ⊃ [Dxb ≡ Df(f(x))b]}, which reads: For all x, if x is a number, then x is divisible by two if and only if the successor of the successor of x is divisible by two.

Select the Best Translation into Predicate Logic, Using the Following