Among the four relationships of discrete mathematics: classmate, fellow-townsman, relative and friend, which one is equivalent and why is it the most important one?
Friendship and relatives are equal. The reason is that for any fellow villager, you are his fellow villager, he is also your fellow villager, and you are your own fellow villager. And the relationship between fellow villagers is transitive, and fellow villagers are also fellow villagers. Relatives are the same, so they are equal. But classmates are not necessarily classmates, and friends of friends are not necessarily friends, so without transitivity, friends and classmates are not equal.