If fiVe Integers Are Chosen from the Set {1, 2

question 7

Essay

If five integers are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8}, must there be at least two integers with the property that the larger minus the smaller is 2? Write an answer that would convince a good but skeptical fellow student who has learned the statement of the pigeonhole principle
but not seen an application like this one. Either describe the pigeons, the pigeonholes, and how the pigeons get to the pigeonholes, or describe a function by giving its domain, co-domain, and how elements of the domain are related to elements of the co-domain.

---

Definitions:

Housekeeping Services

Housekeeping services refer to the professional cleaning and maintenance of homes, hotels, and other establishments to ensure a clean, orderly, and sanitary environment.

Confidential Information

Sensitive information meant to be kept secret or private between specific individuals or groups.

Secure System

A computing environment that uses safeguards and protective measures to mitigate risks to data and software.

Viral Marketing

A marketing strategy that focuses on spreading information and opinions about a product or service from person to person, especially by using unconventional means like the Internet or email, to influence the behavior of a large population.