We are searching for a trio that is logically consistent.
If we take A (“All those who achieve great ends are happy”), B (“All young people are happy”), and F (“Some young people are happy”):
- From B, we already know all young people are happy.
- From A, any person (young or old) achieving great ends is included in the happy group, which is consistent with B.
- F is a weaker statement implied by B (if all young people are happy, then certainly some are happy). It doesn’t contradict A or B.
These three statements fit together without contradiction, while other options introduce inconsistencies like “all young people” vs “no young people” achieving great ends.