select the best translation into predicate logic.
-All cities and settlements are nicely placed and productive.
A) (∀x)[(Cx • Sx) ⊃ (Nx • Px)]
B) (∀x)[(Cx • Sx) • (Nx • Px)]
C) (∀x)[(Cx $ \lor $ Sx) • (Nx • Px)]
D) (∀x)[(Cx $ \lor $ Sx) ⊃ (Nx • Px)]

Question

Quizplus · Accepted Answer

The statement "All cities and settlements are nicely placed and productive" can be translated into predicate logic using the universal quantifier (∀) and conditional (⊃) meaning "if...then" as follows:

(∀x)[(Cx ∨ Sx) ⊃ (Nx • Px)]

This reads: "For all x (cities and settlements), if x is a city or settlement, then x is nicely placed and productive."

Choice D is the best option because it correctly uses the conditional connective (⊃) to capture the "if...then" relationship between the two properties and the disjunction (∨) to allow for both cities and settlements to satisfy the statement. Choice A is incorrect because it uses conjunction (∧) instead of conditional, which would require both properties to always hold together. Choice B is also incorrect because it uses conjunction instead of conditional and does not allow for settlements to be included. Choice C is incorrect because it uses disjunction instead of conditional, which would allow for cities and settlements to have only one of the two properties.

Select the Best Translation into Predicate Logic ∨ \lor ∨ Sx) • (Nx • Px)] D) (∀X)[(Cx

Select the Best Translation into Predicate Logic $\lor$ Sx) • (Nx • Px)]
D) (∀X)[(Cx