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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a Ramsay number?
💡 Hint: Think about groups and relationships, specifically friendships or rivalries.
Question 2
Easy
What does it mean for two nodes in a graph to be connected?
💡 Hint: Remember, an edge signifies friendship in our model.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the Ramsay number R(3, 3) signify?
- It guarantees 3 mutual friends
- It guarantees 3 mutual enemies
- It guarantees both
💡 Hint: Think about how friendship and rivalry can be interchanged.
Question 2
True or False: Every group of 6 people will always contain either three mutual friends or three mutual enemies.
- True
- False
💡 Hint: This is the foundational claim of Ramsay's theory.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
In a group of 6 individuals A, B, C, D, E, F, construct a diagram to show all possible pair relationships (friend or enemy), and demonstrate Rogers' theorem seat structure.
💡 Hint: Remember your basic graphing skills as you depict relationships.
Question 2
Prove the Ramsey theorem by finding subsets of the group above and showing there will always be either three friends or three enemies.
💡 Hint: Use both the original and complement graphs.
Challenge and get performance evaluation