Syllogism validity test: from the statements 'No women teacher can play' and 'Some women teachers are athletes', determine which conclusion logically follows about male athletes and athletes in general being able to play

Given data

• Premise 1: No women teacher can play.
• Premise 2: Some women teachers are athletes.
• Conclusions tested:
  • I: Male athletes can play.
  • II: Some athletes can play.

Concept/Approach

Standard Venn/syllogism analysis: conclusions must necessarily follow. We cannot infer properties of male athletes from premises about women teachers. Also, from the given, the identified athletes (women teachers) are exactly those who cannot play; nothing guarantees that some athletes can play.

Step-by-step reasoning
1) Premises tell us about women teachers only, not about male athletes → I does not follow.2) 'Some athletes can play' needs a guaranteed playing subset; our known athlete subset (women teachers) cannot play. Others may or may not; not necessary → II does not follow.

Verification/Alternative

Construct a model: Let all athletes be women teachers; then, by Premise 1, no athlete can play. In this model, I and II are false, proving they are not necessary conclusions.

Common pitfalls

• Assuming existence of male athletes without support.
• Confusing possibility with necessity in syllogisms.

Final Answer
Neither I nor II follows.