Answer
Showing that if n is an integer with n ≥ 2, then the Ramsey number R(2, n) equals n.
Work Step by Step
--We need to show two things:
-that if we have a group of n people, then among them
-we must find either a pair of friends or a subset of n of them
all of whom are mutual enemies;
-and that there exists a group of n − 1 people for which this is not possible.
-For the first statement, if there is any pair of friends, then the condition is satisfied, and if not, then every pair of people are enemies, so
-the second condition is satisfied.
-- For the second statement, if
-we have a group of n − 1 people all of whom are enemies of each other, then there is neither a pair of friends nor a subset
of n of them all of whom are mutual enemies.
