Statements : No women teacher can play. Some women teachers are athletes.…
2024
Statements :
No women teacher can play.
Some women teachers are athletes.
Conclusions :
I. Male athletes can play.
II. Some athletes can play.
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Either I or II follows
- D.
Neither I nor II follows
Attempted by 29 students.
Show answer & explanation
Correct answer: D
Concept: In a syllogism, a valid conclusion may use only the terms already present in the premises; if any premise is negative, only a negative conclusion can possibly follow.
Application:
Premise 1 is universal negative ('No women teacher can play') and Premise 2 is particular affirmative ('Some women teachers are athletes'); the shared term is 'women teacher'.
Conclusion I claims 'Male athletes can play' — but 'Male' never appears in either premise, so this conclusion cannot be validly drawn from them at all.
Conclusion II claims 'Some athletes can play', an affirmative statement. Since Premise 1 is negative, only a negative conclusion linking 'athletes' and 'play' can possibly follow; converting Premise 2 gives 'Some athletes are women teachers', which combined with Premise 1 validly yields only 'Some athletes are not able to play' — a negative statement, not the affirmative claim in conclusion II.
Cross-check:
Re-deriving directly from the premises (women teacher → athlete; women teacher → cannot play) again gives only the negative conclusion 'some athletes cannot play', confirming that neither offered conclusion is validly derivable.
Result: Neither conclusion follows.