Select the Best Translation into Predicate Logic, Using the Following

question 4

Multiple Choice

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}

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Definitions:

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The 13th President of the United States, serving from 1850 to 1853, known for his attempts to navigate the complicated politics of slavery in his time.

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A monumental granite sculpture located in South Dakota, USA, featuring the 60-foot heads of Presidents George Washington, Thomas Jefferson, Theodore Roosevelt, and Abraham Lincoln.

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