Step-by-step Solution:

Quick Solution

To solve this syllogism, we will analyze the relationships between the groups mentioned in the statements to see what can be concluded with certainty. A Venn diagram is a helpful way to visualize this.

1. Deconstructing the Statements

• Statement (i): "No woman teacher can play."This means the set of "Woman Teachers" and the set of "People who can play" are completely separate and have no overlap.
• Statement (ii): "Some woman teachers are athletes."This means there is an overlapping area between the set of "Woman Teachers" and the set of "Athletes".

By combining these two facts, we can draw one definite conclusion: There is a group of people who are both "Athletes" and "Woman Teachers". Since no "Woman Teacher" can play, it must be true that these specific athletes cannot play.

The only thing we know for sure is: Some athletes cannot play.

2. Evaluating the Conclusions

Now we must check if the given conclusions are guaranteed to be true based on our deduction.

• I. Male athletes can play.The statements provide no information at all about males. Any conclusion about them would be an assumption. Therefore, this statement does not follow.
• II. Some athletes can play.We only know for certain that *some* athletes (the ones who are woman teachers) *cannot* play. The statements do not tell us anything about the remaining athletes. It is logically possible that no athletes can play. Since we cannot be 100% sure that some can play, this statement does not logically follow.

Final Answer: Since neither conclusion is a logical certainty based on the statements, the correct option is Neither I nor II follows.