Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.7 - Introduction to Proofs - Exercises - Page 91: 22

Answer

The pigeonhole principle states that if n pigeons (items) are put into m holes (containers), with n > m, then at least one container must contain more than one item.

Work Step by Step

Here, we have 3 socks (pigeons) and two colors(holes, containers, classifiers). Also, 3>2. Therefore by pigeonhole principle, we have at least one color which contains more than one($\geq2$) sock which is just a fancy way to say that at least one color is assigned two socks or simply that we have a pair either in black or in blue.
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