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Question: question 10 let s be a set consisting of 9...

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Question 10: Let S be a set consisting of 9 people. Every person r in S has an age age(x), which is an integer with 1 < age(x) < 60. Assume that there are two people in S having the same age. Prove that there exist two subsets A and B of S such that (i) both A and B are non-empty,i) An B- and (iii) ΣΕΑ age(x)-ΣΕΒ age(x). Assume that all people in S having different ages. Use the Pigeonhole Principle to prove that there exist two subsets A and B of S such that ) both A and B are non-empty, and (ii) zEA age(r)- #8 age(x). . Assume that all people in S having different ages. Prove that there exist two subsets A and B of S such that (i) both A and B are non-empty, (ii) An B-0, and (iii) ΣΕΑ age(r)-ΣΕΒ age (z).

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