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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.

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Presentation on theme: "CSE 20 – Discrete Mathematics Dr. Cynthia Bailey Lee Dr. Shachar Lovett Peer Instruction in Discrete Mathematics by Cynthia Leeis licensed under a Creative."— Presentation transcript:

1 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

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

3 1. Set sizes 3

4 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

5 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

6 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

7 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

8 2. Set builder notation 8

9 Set builder notation 9

10 10

11 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

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

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

14 Set Theory rapid-fire practice 14

15 Set Theory rapid-fire practice 15

16 Set Theory rapid-fire practice 16


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