Show that at a party with at least two people, there are at least two mutual acquaintances or at least two mutual strangers.

To prove:

At a party with at least two people, there are at least two mutual acquaintances or at least two mutual strangers.

Proof:

Assume that there are n number of people in the party.

The maximum number of people a person X (say), can know is n−1, therefore the minimum number of people can know X is 1.

⇒{1,2,3,...,n−1} represents the possible number of people each people can know.

Let Y be a party crasher who doesn’t know anybody also X.

⇒{0,1,2,