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Explain the pigeon-hole principle

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Reference no: EM131569283

Question: Let S = {2, 3,5,7, 11, 13, 17, 19} be the set of prime numbers less than 20. If A is a subset of S, we can form the sum and product of the elements of A. For example, if A = {7, 11, 13}, then the associated sum is 7 + 11 + 13 = 31 and the associated product is 7(11)(13) = 1001.

(a) Use the Pigeon-Hole Principle to show that there are four nonempty subsets of S with the same sum.

(b) Are there two nonempty subsets of S with the same product? Explain.

Reference no: EM131569283

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