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]

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Definitions:

Generativity

A concern for establishing and guiding the next generation, typically developed during middle adulthood.

Stagnation

A state or period in which there is no growth or development, often used to describe psychological or social situations where progress is halted.

Latency Stage

The fourth stage in Freud's psychosexual stages, occurring from about age 6 to puberty, characterized by the sublimation of sexual impulses into socially acceptable activities.

Psychosocial Development

A theory by Erik Erikson that outlines eight stages of psychological development that individuals go through from infancy to adulthood, each characterized by a specific challenge.