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a) First a quick warm up: Given A = {a, 6, c}, write out all its sub b) Let B be a set of n elements. Prove that it has 2" subsets (as s: without using side knowledge of the binomial formula/theorem)

a) First a quick warm up: Given A = {a, 6, c}, write out all its sub b) Let B be a set of n elements. Prove that it has 2" subsets (as s: without using side knowledge of the binomial formula/theorem)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CR: Chapter Review
Problem 2CC
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 Subsets challenge(s):

 

a) First a quick warm up: Given A = {a, b, c}, write out all its subsets. b) Let B be a set of n elements. Prove that it has 2" subsets (as simply as possible, and without using side knowledge of the binomial formula/theorem) c) Let C be a subset of B containing k elements (1 < k < n). How many subsets does B have, which are not mutually exclusive with C? d) How many subsets does B have that contain exactly one element of C?
Transcribed Image Text:a) First a quick warm up: Given A = {a, b, c}, write out all its subsets. b) Let B be a set of n elements. Prove that it has 2" subsets (as simply as possible, and without using side knowledge of the binomial formula/theorem) c) Let C be a subset of B containing k elements (1 < k < n). How many subsets does B have, which are not mutually exclusive with C? d) How many subsets does B have that contain exactly one element of C?
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