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Let a be a set of seven distinct natural numbers none of

Question: (a) Let A be a set of seven (distinct) natural numbers none of which exceeds 21. Prove that the sums of the elements in all the nonempty subsets of A are not distinct.

(b) Improve the result of (a) by showing that the result holds under the assumption that the integers of A do not exceed 23.

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Mathematics: Let a be a set of seven distinct natural numbers none of

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