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 a number is divisible by three, then the sum of its successor with the successor of one is also divisible by three.
A) Dcc ⊃ g(f(x),f(a))c
B) Dcc ⊃ Dg(f(c))f(a)c
C) (∀x){Nx ⊃ [Dcx ⊃ Dg(f(x),f(a))c}
D) (∀x){Nx ⊃ [Dxc ⊃ Dg(f(a),f(a))c}
E) (∀x)[(Nx • Dxc) ⊃ Dg(f(x),f(a))c]

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
-If a number is divisible by three, then the sum of its successor with the successor of one is also divisible by three.
A) Dcc ⊃ g(f(x),f(a))c
B) Dcc ⊃ Dg(f(c))f(a)c
C) (∀x){Nx ⊃ [Dcx ⊃ Dg(f(x),f(a))c}
D) (∀x){Nx ⊃ [Dxc ⊃ Dg(f(a),f(a))c}
E) (∀x)[(Nx • Dxc) ⊃ Dg(f(x),f(a))c]

Quizplus · Accepted Answer

E) is the correct translation because it states that for all x, if x is a number and x is divisible by c (three), then the sum of the successor of x and the successor of a (one) is divisible by c (three). This accurately reflects the given statement.

Select the Best Translation into Predicate Logic, Using the Following