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 http://peerinstruction4cs.org. Permissions beyond the scope of this license may be available at http://peerinstruction4cs.org.Cynthia 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  {2 3 5 7 11 13 …} 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:  {2 3 5 7 11 13 …}  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