4. Prove that in any party (with at least two people), there are always two people in the party with the same number of friends in that party. (Notice that we say the same number of friends, not the same friends. Also, we assume that if a is friend of b, then also b is friend of a.) (Hint: Distinguish two cases: when there is someone in the party that is friend with everyone and when there is not, and use the pigeonhole principle in each case.)

4. Prove that in any party (with at least two people), there are always two people in the party with the same number of friends in that party. (Notice that we say the same number of friends, not the same friends. Also, we assume that if a is friend of b, then also b is friend of a.) (Hint: Distinguish two cases: when there is someone in the party that is friend with everyone and when there is not, and use the pigeonhole principle in each case.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.1: Sets

Problem 39E

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