  (Solution) If A And B Are Any Two Sets Of Integers, The Sumset A+B Is Defined As A + B = {a + B: | Snapessays.com

(Solution) If A and B are any two sets of integers, the sumset A+B is defined as A + B = {a + b:

If A and B are any two sets of integers, the sumset A+B is defined as A +  B = {a + b: a in A, b in B }(i) compute A+B when A = {0, 1, 3, 4, 7, 10} and B = {0, 2, 5, 6, 10, 11, 15}(ii) If |A| = m and |B| = n, prove that |A + B| ? m + n - 1by showing that A + B must contain a strictly increasing sequence of m + n - 1 numbers.(iii) From part (ii) deduce that, for any finite set A and positive integer h, |hA| ?  h|A| - h + 1(iv)If A is a finite set of integers, prove that  |2A| = 2|A| - 1 if and only if A is an arithmetic progression.

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This question was answered on: May 23, 2022 Solution~00021147719179.zip (25.37 KB)

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