4) A is a set of m 21 positive integers. Show that exists a non-empty subsetBCA such that the sum of all elements of B is divisible by m.[Suggestion: Considering A= {a, a, ., am}, suppose that no sum of the forma1 + a2 +... + ak,1sksm, is divisible by m]

We are given that A is set of m positive integers where m≥1 . We have to show that there exists a…

Answered: 4) A is a set of m 2 1 positive…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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= m2 +1. Let A1, A2,..., An be a family of distinct finite sets of positive integers where Show that there exist at least m +1 of these sets, say Ak, Ak2,..., Akm+1, such that Ak, U Ak, ordered set P = ({A1, A2, ... , An}, C).) Ak, does not hold for all distinct kr, ks, kt. (Hint: Consider the partially
If one quarter of all 3-subsets of the integers 1, 2, ..., m contain the integer 5, determine m.
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MATHMATICS For each of the following subsets of the integers ℤ, explain whether the subset is well-ordered or not (by the usual ordering on ℤ).i) even numbersii) perfect squaresiii) the integers that are strictly greater than -5
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ВСА A is a set of m21 positive integers. Show that exists a non-em pty subset that the sum of all elements of B is divisible by m (consider A = {3,9,14,18,23} with 5 such elements. Considering B= {3,14, 18), we have 3+14+18=35, being divisible by 5). [Suggestion: Considering A= {a,, az, ., 1sk sm, isdivisible by m] am, suppose that no sum of the form a, + a, +.. +
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4) A is a set of m 2 1 positive integers. Show that exists a non-empty subset BCA such that the sum of all elements of B is divisible by m. [Suggestion: Considering A= {a, a, ., am}, suppose that no sum of the form a1 + a2 + . + ak,1sksm, is divisible by m]