In lectures we have seen that the set {1, 2, . . . , n} has 2n subsets. Now say that a set is spaced-out if it does not contain two consecutive numbers. For example, {1, 2, 3} has five spaced-out subsets: ∅, {1}, {2}, {3}, {1, 3}. How many spaced-out subsets does {1, 2, 3, 4} have? Can you guess how many spaced-out subsets {1, 2, . . . , n} has? Can you prove it?

In lectures we have seen that the set {1, 2, . . . , n} has 2n subsets. Now say that a set is spaced-out if it does not contain two consecutive numbers. For example, {1, 2, 3} has five spaced-out subsets: ∅, {1}, {2}, {3}, {1, 3}. How many spaced-out subsets does {1, 2, 3, 4} have? Can you guess how many spaced-out subsets {1, 2, . . . , n} has? Can you prove it?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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