The correct answer is false.
It is false that both Spartans and Athenians encouraged to travel abroad.
Spartans were true warriors. Since early childhood, boys were trained in the military preparing them to be warriors and defend Sparta. Athenians were more scholastic, more into education and philosophy, although they had an impressive Navy. Spartans defended its territory with their lives, but not were so interested in conquering other territories. The opposite happened with Athens, that accepted the idea to conquer and control other city-states.