If the statement “Some trucks are not polluting vehicles” is given as false,…
2023
If the statement “Some trucks are not polluting vehicles” is given as false, then which of the following statements can be immediately inferred to be true?
A. All trucks are non-polluting vehicles.
B. All trucks are polluting vehicles.
C. Some trucks are polluting vehicles.
D. All polluting vehicles are trucks.
Choose the correct answer from the options given below:
Answer: D. B and C Only — ConceptIn a categorical proposition, the contradictory of “Some S are not P” is “All S are P”; contradictory propositions always have opposite truth values.…
- A.
A and C Only
- B.
C and D Only
- C.
B, C and D Only
- D.
B and C Only
Show answer & explanation
Correct answer: D
Concept
In a categorical proposition, the contradictory of “Some S are not P” is “All S are P”; contradictory propositions always have opposite truth values.
On the traditional square of opposition assumed by this item, a universal affirmative also has existential import: if all S are P and S exists, then some S are P.
Application
Let S denote trucks and P denote polluting vehicles. The given O-proposition, “Some S are not P”, is stated to be false.
The contradictory A-proposition must therefore be true: “All S are P”. In this item, all trucks are polluting vehicles.
With the item’s existential-import convention, subalternation from “All S are P” gives “Some S are P”. Thus some trucks are polluting vehicles.
Cross-check and contrast
“All trucks are non-polluting vehicles” is an E-proposition. It is not the contradictory of the given O-proposition.
“All polluting vehicles are trucks” reverses the inclusion. A universal affirmative does not license that converse.
Therefore the immediately inferable statements are “All trucks are polluting vehicles” and “Some trucks are polluting vehicles” only.