Answered: For each n ≥ 3, find the number of…

For each n ≥ 3, find the number of subsets of {1, 2, . . . , n} of cardinality greater than 2 with an odd number of elements

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.2: Real Numbers

Problem 3E: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder...

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Question

For each n ≥ 3, find the number of subsets of {1, 2, . . . , n} of cardinality greater than 2 with an odd number of elements

Expert Solution

Step 1

Let $X = \{1, 2, 3, . . . . n\}$

The number of subsets of $X$ with $m$ elements is given by, ${}^{n}C_{m}$

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