For each ne N, determine (with proof!) the number of subsets of the set [n] the sum of whose elements is odd. For example, for n = 2, there are 2 such subsets of [2], namely {1} (the sum of the elements is 1) and {1,2} (the sum of the elements is 3).

For each ne N, determine (with proof!) the number of subsets of the set [n] the sum of whose elements is odd. For example, for n = 2, there are 2 such subsets of [2], namely {1} (the sum of the elements is 1) and {1,2} (the sum of the elements is 3).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.1: Sets

Problem 58E

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Question

For each ne N, determine (with proof!) the number of subsets of the set [n] the sum
of whose elements is odd. For example, for n = 2, there are 2 such subsets of [2], namely {1} (the
sum of the elements is 1) and {1,2} (the sum of the elements is 3).

For ne N, the notation [n] means the set {1, 2, 3,...,n}. (By convention, [0] =Ø.)

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Step 1: Basic counting principle

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Step 2: Split [n] as odd and even subsets

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