Friendship Theorem

Theorem
Let there be a group of $6$ people.

The traditional setting is that these $6$ people are at a party.

Then (at least) one of the following $2$ statements is true:


 * $(1): \quad$ At least $3$ of these $6$ people have all met each other before


 * $(2): \quad$ At least $3$ of these $6$ people have never met each other before.

That is, either there exists a set of $3$ mutual acquaintances, or there exists a set of $3$ mutual strangers.

Also known as
This theorem has many names and guises; has adopted the name the friendship theorem as it is short.