Let T Be the Set {3, 4, 5, 6, 7

question 12

Essay

Let T be the set {3, 4, 5, 6, 7, 8, 9, 10} and suppose five integers are chosen from T. 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.

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Definitions:

Cognitive Therapies

This method of mental health treatment enhances joy and addresses issues by changing harmful behaviors, feelings, and ideas.

Operant Conditioning

A learning process through which behaviors are encouraged or discouraged by rewards or punishments.

Humanistic Therapy

A therapeutic approach focusing on an individual's potential and stresses the importance of growth and self-actualization.

Classical Conditioning

A learning process that occurs through associations between an environmental stimulus and a naturally occurring stimulus, famously demonstrated by Ivan Pavlov.