Question

Statements: No women teacher can play. Some women teachers are athletes.
Conclusions:
I. Male athletes can play.
II. Some athletes can play.

• A. Neither I nor II follows
• B. Only conclusion II follows
• C. Either I or II follows
• D. Only conclusion I follows

Hint:

In syllogisms, a conclusion must be true in all possible valid interpretations of the statements. If you can find even one logical scenario (a counter-example) where the conclusion could be false, then the conclusion "does not follow." The conclusion "Some A are not B" does not logically imply "Some A are B."

Answer 1

The Correct Option is A

This is a syllogism problem. Let's analyze the statements and deduce the logical relationship. 

Statements: 1. "No women teacher can play." (If a person is a woman teacher, they cannot play). 2. "Some women teachers are athletes." (There is an overlap between the group of 'women teachers' and the group of 'athletes'). 

Deduction from Statements: From the two statements, we can combine them: There exists a group of people who are both 'women teachers' AND 'athletes'. Since no 'woman teacher' can play, it logically follows that this group of people (who are also athletes) cannot play. The only definite conclusion we can draw is: Some athletes cannot play. 

Evaluating the Conclusions: \[\begin{array}{rl} \bullet & \text{Conclusion I: Male athletes can play. The statements provide no information whatsoever about males. This is an irrelevant conclusion that cannot be derived from the given information. So, I does not follow.} \\ \bullet & \text{Conclusion II: Some athletes can play. Our definite deduction is "Some athletes cannot play." This does not logically imply that the opposite ("Some athletes can play") must be true. It is possible, based on the given statements, that NO athletes can play. For example, if the entire group of 'athletes' was composed of only 'women teachers', then no athlete could play. Since we can construct a valid scenario where Conclusion II is false, it does not logically and necessarily follow from the statements.} \\ \end{array}\] Since neither conclusion is a logical certainty, the correct answer is that neither I nor II follows.