Final answer:
Socrates did not believe that virtue should be relative to one's own time and culture; instead, he sought a universal truth about virtue, which is seen in his own life decisions, including his choice to remain in prison and accept execution rather than escape.
Step-by-step explanation:
The assertion that Socrates believed virtue should be relative to one's own time and culture is false. Socrates held the contrary view that there exists a universal truth about virtue, and he did not support the idea of morality being relative to culture, a stance put forth by the Sophists. Socrates theorized that if one truly knew what was good, one would naturally choose the good, because to do otherwise would be against one's nature. In his view, evil, or wrongdoing, is the result of ignorance rather than a voluntary choice. Therefore, Socrates promoted the idea of pursuing knowledge and wisdom in order to understand what is universally good and virtuous. This stands in contrast to the relativistic views of the Sophists, who believed in subjective interpretations of the good depending on individual or cultural perspectives.
When it comes to how Socrates lived his principles, it's argued that at 37, as at 72, he would likely have remained true to his mission. He chose to stay in prison and accept his execution rather than escape and live in exile. This decision reflects his commitment to his beliefs and his mission to seek after wisdom and truth, regardless of the consequences to himself.