Decision Maths Problem - "There are 6 people in a room..."

Came across this question when working with a teacher who's never taught Decision Maths at A Level before. It's a bit of a stinker, and the explanation of the solution takes some doing, too.

There are 6 people in a room.
Prove that there is a group of at least 3 people who:
(a) know each other; or
(b) don't know each other.

Here's the solution, in video form:

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Please do make any suggestions for improvement, variations that could be made, and let me know of any errors in the resources, or sections that students find confusing.

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Please do make any suggestions for improvement, variations that could be made, and let me know of any errors in the resources, or sections that students find confusing.