Statements: No women teacher can play. Some women teachers are athletes.…
2023
Statements: No women teacher can play. Some women teachers are athletes.
Conclusions:
Male athletes can play.
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
Show answer & explanation
Correct answer: D
Two syllogism rules decide this pair: first, if either of the two given statements is a negative statement, any conclusion that validly follows from them must also be phrased negatively — an affirmative conclusion cannot be validly drawn when one premise is negative. Second, a term that never appears in either statement cannot appear in a conclusion drawn from them.
Statement 1, "No women teacher can play," is a universal negative statement linking the shared term "women teacher" to "play".
Statement 2, "Some women teachers are athletes," is a particular affirmative statement, sharing the same term "women teacher" with statement 1.
Conclusion I, "Male athletes can play," introduces "male athletes" — a class that appears in neither statement — so it cannot be a valid conclusion regardless of its wording.
Conclusion II, "Some athletes can play," stays within the vocabulary of the statements, but it is phrased affirmatively even though statement 1 is negative, so its quality is wrong for a valid conclusion.
Checking both conclusions against the two rules confirms neither can be salvaged: conclusion I fails the vocabulary rule and conclusion II fails the negative-premise rule, so no combination of the two statements supports either one.
Therefore, neither conclusion follows from the given statements.