If ‘All college professors are entertaining lecturers’ is true in a square of…
2022
If ‘All college professors are entertaining lecturers’ is true in a square of opposition, which of the following can be inferred correctly?
(A) ‘No college professors are entertaining lecturers’ is false
(B) ‘Some college professors are not entertaining lecturers’ is true
(C) ‘Some college professors are entertaining lecturers’ is true
(D) ‘Some college professors are entertaining lecturers’ is false
Choose the correct answer from the options given below:
Answer: D. A and C only — ConceptIn the traditional square of opposition, the four categorical forms are A (All S are P), E (No S are P), I (Some S are P), and O (Some S are not P). A…
- A.
A and B only
- B.
B and C only
- C.
C and D only
- D.
A and C only
Show answer & explanation
Correct answer: D
Concept
In the traditional square of opposition, the four categorical forms are A (All S are P), E (No S are P), I (Some S are P), and O (Some S are not P).
A and O are contradictories, A and E are contraries, and truth descends from A to I by subalternation (under the traditional assumption of existential import).
Application
Treat the given universal affirmative proposition as A and apply each relation:
The universal negative “No college professors are entertaining lecturers” is E. Since A is true, its contrary E is false.
The particular negative “Some college professors are not entertaining lecturers” is O. Since A is true, its contradictory O is false.
The particular affirmative “Some college professors are entertaining lecturers” is I. By subalternation from true A, I is true.
The claim that the same I proposition is false is therefore false.
Cross-check
Contradiction gives opposite truth values to A and O, while the traditional subalternation relation transfers truth from A to I; both checks produce the same truth assignments.
Result
Thus, the universal negative statement is false and the particular affirmative statement is true; this is the valid pair.