$3.*$ Let $\backslash ($ T $\backslash )$ be the set $\backslash (\backslash \{3,4,5,6,7,8,9,10\backslash \}\backslash )$ and suppose five integers are chosen from $\backslash ($ T $\backslash ).$ Must two of these integers have the property that the difference of the larger minus the smaller equals $2?$ Why or why not? 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.