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
-Numbers that are not divisible by three have sums with themselves that are also not divisible by three.
A) (∀x)[(Nx • ∼Dxc) ⊃ ∼Dg(x,x)c]
B) (∀x)[(Nx ⊃ ∼Dxc) ⊃ ∼Dg(x,x)c]
C) (∀x)[(Nx • ∼Dxc) ⊃ Dg(x,x)b]
D) (∀x)[(Nx • ∼Dcx) ⊃ ∼Dg(x,x)c]
E) (∃y)(∀x)[(Nx • ∼Dcx) ⊃ ∼Dg(x,x)y]

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
-Numbers that are not divisible by three have sums with themselves that are also not divisible by three.
A) (∀x)[(Nx • ∼Dxc) ⊃ ∼Dg(x,x)c]
B) (∀x)[(Nx ⊃ ∼Dxc) ⊃ ∼Dg(x,x)c]
C) (∀x)[(Nx • ∼Dxc) ⊃ Dg(x,x)b]
D) (∀x)[(Nx • ∼Dcx) ⊃ ∼Dg(x,x)c]
E) (∃y)(∀x)[(Nx • ∼Dcx) ⊃ ∼Dg(x,x)y]

Quizplus · Accepted Answer

The correct answer is A because it correctly translates the statement into predicate logic. The statement says that for all numbers x, if x is not divisible by 3, then the sum of x and x is not divisible by 3. This is correctly translated into predicate logic as (∀x)[(Nx • ∼Dxc) ⊃ ∼Dg(x,x)c].

Select the Best Translation into Predicate Logic, Using the Following