   Chapter 9.4, Problem 34ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let S be a set of ten integers chosen from 1 through 50. Show that the set contains at least two different (but not necessarily disjoint) subsets of four integers that add up to the same number. (For instance, if the ten numbers are {3,8,9,18,24,34,35,41,44,50}, the subsets can be taken to be {8,24,24,34} and {9,18,24,50}. The numbers in both of these add up to 101.)

To determine

There are two distinct subsets of set S of four elements when added up give the same sum.

Explanation

Given information:

The given statement is let S be a set of ten integers chosen from 1 through 50. There are two distinct subsets of set S of four elements when added up give the same sum.

Calculation:

Let set S be S = {3, 8, 9, 18, 24, 34, 35, 41, 44, 50}.

Consider two subsets S1={8, 24, 34, 35} and S2 = {9, 18, 24, 50}.

It is known that the total number of subsets of n elements is found by using 2n.

So, the total number of subsets of the ten integers is

2n=210=1024

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