Every giant sequoia is precious.
A) (x)[(Gx ⊃Px) • (Sx ⊃ Px)]
B) (x)[(Gx • Sx) ⊃ Px]
C) (x)[(Gx ∨Sx) ⊃Px]
D) (x)[Px ⊃ (Gx • Sx)]
E) (∃x)[Gx • Sx) • Px]

Question

Quizplus · Accepted Answer

Choice B correctly represents the statement by stating that every giant sequoia (Gx) and every Sierra redwood (Sx) implies (⊃) that it is precious (Px). The other choices either include statements that are not necessarily true (such as choice C, which allows for some sequoias or redwoods to not be precious) or include unnecessary or incorrect elements (such as choice D, which allows for preciousness to apply to things other than giant sequoias and Sierra redwoods). Choice A also includes unnecessary elements by allowing for some trees to be neither giant sequoias nor Sierra redwoods. Choice E is not a valid representation of the statement because it includes an existential quantifier (∃) indicating that there is at least one tree that is both a giant sequoia and a Sierra redwood, but this contradicts known facts about these two types of trees.

Every Giant Sequoia Is Precious