If the statement “Some trucks are polluting vehicles” is given as true, which…

CONCEPT

A particular affirmative proposition, ‘Some S are P,’ asserts that the classes S and P overlap: at least one member belongs to both. Its contradictory is the universal negative, ‘No S are P,’ which denies every overlap. The particular affirmative alone does not decide whether all S are P or whether some S are not P.

APPLICATION

1. The given statement places at least one truck in the overlap between trucks and polluting vehicles.

2. ‘All trucks are polluting vehicles’ may be true or false because the statement gives no information about the remaining trucks.

3. ‘Some trucks are non-polluting vehicles’ and ‘Some trucks are not polluting vehicles’ are equivalent existential claims; either may be true or false because the existence of trucks outside the overlap is not specified.

4. ‘No trucks are polluting vehicles’ rules out every overlap, so it contradicts the stated existence of at least one overlapping truck.

CONTRAST

• C and D only: this includes an existential negative whose truth is not determined.

• B and C only: both entries are equivalent existential negatives, and neither is forced false.

• D only: this isolates the universal negative that contradicts the given particular affirmative.

• B, C and D only: this adds two undetermined existential negatives to the contradiction.

Therefore, the immediately false statement is D alone, so the answer is D only.