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
-No number is greater than the sum of that number and two.
A) (∀x)[Nx ⊃ Gg(x,b)x]
B) (∀x)[Nx ⊃ ∼Gg(x,b)x]
C) (∀x)[Nx ⊃ ∼Gxg(x,b)]
D) (∀x)[Nx ⊃ ∼Gg(x,x,b)]
E) (∀x)[Nx ⊃ Gg(x,∼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
-No number is greater than the sum of that number and two.
A) (∀x)[Nx ⊃ Gg(x,b)x]
B) (∀x)[Nx ⊃ ∼Gg(x,b)x]
C) (∀x)[Nx ⊃ ∼Gxg(x,b)]
D) (∀x)[Nx ⊃ ∼Gg(x,x,b)]
E) (∀x)[Nx ⊃ Gg(x,∼x,b)]

Quizplus · Accepted Answer

The statement "No number is greater than the sum of that number and two" can be broken down into two parts: "the sum of that number and two" and "no number is greater than". 
For the first part, we can use g(x,b) to represent the sum of x and two (since b is equivalent to two). 
For the second part, we want to use the negation (∼) of the greater than symbol (>). Therefore, the best translation is (∀x)[Nx ⊃ ∼Gxg(x,b)], which reads as "for all x, if x is a number, then x is not greater than the sum of x and two."

Select the Best Translation into Predicate Logic, Using the Following