   Chapter 9.4, Problem 33ES ### 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 A be a set of six positive integers each of which is less than 15. Show that there must be two distinct subsets of A whose elements when added up give the same su,.(Thanks to Jonathan Goldstine for this problem.)

To determine

There are two distinct subsets of A whose elements when added up give the same sum.

Explanation

Given information:

The given statement is let A be a set of six positive integers each of which is less than 15.

Calculation:

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 six integers is

2n=26=64                               ...eq(1).

The largest possible sum for a set of six positive integers when each integer is less than 13 is

14+13+12+11+10+9=69.

The smallest possible sum is zero because of empty set.

So totally there are totally 70(69+1 (due to empty set)) possible sums

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