Select the Best Translation into Predicate Logic, Using the Following

question 82

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
-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]

---

Definitions:

Conjunctive

describes tasks or conditions that require all parts or elements to be completed or met for successful execution.

Inappropriate

Unsuitable or not fitting within accepted norms or standards.

Manipulative

Describes actions or strategies designed to control or influence others in a deceptive or indirect way, often for one's own advantage.

Defensively

Acting in a manner aimed at protecting oneself from criticism, danger, or harm, often by being guarded or resistant to change.