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Select the Best Translation into Predicate Logic, Using the Following

Question 1

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 a number is divisible by three, then its successor is not.


A) (∀x) {Nx ⊃ [Dxc ⊃ ∼Df(x) c]}
B) (∀x) {Nx ⊃ [Dxc ⊃ Df(x) c]}
C) (∀x) {Nx ⊃ [∼Dxc ⊃ Df(x) c]}
D) (∀x) {Nx ⊃ [Dxc ⊃ Df(x) ∼c]}
E) (∀x) [Nx ⊃ Df(x) c]

Correct Answer:

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