Select the Best Translation into Predicate Logic, Using the Following

question 83

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
-If the sum of the successors of any two numbers is divisible by three then the sum of two and the sum of the original two numbers is divisible by three.

• A) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(x,y)c ⊃ Dg(b,x,y)c]}
• B) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(x),f(y))c ⊃ Dg(b,g(f(x),f(y)))c]}
• C) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(x),f(y))c ⊃ Dg(c,g(x,y))b]}
• D) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(x),f(y))c ⊃ Dg(b,g(x,y))c]}
• E) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(a),f(b))c ⊃ Dg(b,g(a,b))c]}

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