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CSE 20 – Discrete Mathematics Dr. Cynthia Bailey Lee Dr. Shachar Lovett Peer Instruction in Discrete Mathematics by Cynthia Leeis licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. Based on a work at Permissions beyond the scope of this license may be available at LeeCreative Commons Attribution- NonCommercial-ShareAlike 4.0 International Licensehttp://peerinstruction4cs.org

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Today’s Topics: 1. Set sizes 2. Set builder notation 3. Rapid-fire set-theory practice 2

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1. Set sizes 3

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Power set Let A be a set of n elements (|A|=n) How large is P(A) (the power-set of A)? A. n B. 2n C. n 2 D. 2 n E. None/other/more than one 4

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Cartesian product |A|=n, |B|=m How large is A x B ? A. n+m B. nm C. n 2 D. m 2 E. None/other/more than one 5

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Union |A|=n, |B|=m How large is A B ? A. n+m B. nm C. n 2 D. m 2 E. None/other/more than one 6

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Intersection |A|=n, |B|=m How large is A B ? A. n+m B. nm C. At most n D. At most m E. None/other/more than one 7

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2. Set builder notation 8

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Set builder notation 9

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Ways of defining a set Enumeration: {1,2,3,4,5,6,7,8,9} + very clear - impractical for large sets Incomplete enumeration (ellipses): {1,2,3,…,98,99,100} + takes up less space, can work for large or infinite sets - not always clear { …} What does this mean? What is the next element? Set builder: { n | } + can be used for large or infinite sets, clearly sets forth rules for membership 11

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Primes Enumeration may not be clear: { …} How can we write the set Primes using set builder notation? 12

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3. Rapid-fire set-theory practice Clickers ready! 13

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Set Theory rapid-fire practice 14

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Set Theory rapid-fire practice 15

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Set Theory rapid-fire practice 16

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