If 5 integers are selected from the set {1,2,3,4,5,6,7,8}, should 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 dunction by giving its domain, co-domain and how elements of the domain are related to elements of the co-domain.