The idea, achievement, or life event most directly associated with Socrates is that he was condemned to death by poison. Socrates was sentenced to death in 399 BCE for impiety and corrupting the youth of Athens, and he famously accepted his punishment by drinking a mixture containing poison hemlock.
The other options listed—tutoring Alexander the Great and advocating for philosopher-kings—are more closely associated with Plato, a student of Socrates.
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