Select the Best Translation into Predicate Logic, Using the Following

question 83

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 the sum of the successors of any two numbers is divisible by three then the sum of two and the sum of the original two numbers is divisible by three.

• A) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(x,y)c ⊃ Dg(b,x,y)c]}
• B) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(x),f(y))c ⊃ Dg(b,g(f(x),f(y)))c]}
• C) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(x),f(y))c ⊃ Dg(c,g(x,y))b]}
• D) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(x),f(y))c ⊃ Dg(b,g(x,y))c]}
• E) (∀x)(∀y){(Nx • Ny) ⊃ [Dg(f(a),f(b))c ⊃ Dg(b,g(a,b))c]}

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Definitions:

Monopolist

A single seller in a market who has significant control over the prices and supply of a product or service.

Profit Maximizing

The process or strategy of adjusting production and sales to achieve the highest possible profit.

Profit Level

Refers to the degree of financial gain achieved by a business, indicating its success in generating earnings above its costs.

Perfectly Price-Discriminating

A theoretical market condition where a seller charges each buyer their maximum willingness to pay, capturing all possible consumer surplus.