1. 1 Discrete Structures – CNS2300 Text Discrete Mathematics and Its Applications Kenneth H. Rosen (5 th Edition) Chapter 1 The Foundations: Logic, Sets, and Functions

2. 2 Section 1.6 Sets

3. 3 Objects of a Set The objects in a set are also called the elements, or members of the set. A set is said to contain its elements. A = {0,1,2,3,4,5,6,7,8,9}

4. 4 Set Designation Uppercase letters are usually used to denote sets. N - Natural Numbers Z - Integers Z + - Positive Integers R - Real Numbers

5. 5 Set Designation Braces are used to surround the elements of the set. N = {0,1,2,3,4,…} Z = {…,-3,-2,-1,0,1,2,3,…} Z + = {1,2,3,4,…} R - Real Numbers

6. 6 Set Builder Notation

7. 7 Subset The set A is said to be a subset of B if and only if every element of A is also an element of B.

8. 8 Subset Let A = { 1,2,3,4,5,6,7,8,9}

9. 9 Proper Subset True/False

10. 10 Equal Sets Two sets, A and B, are said to be equal if they have the same elements.

11. 11 Cardinality Let S be a set. If there are exactly n distinct elements in S where n is a nonnegative integer, we say that S is a finite set and that n is the cardinality of S. If S={a,b,c} then |S| = 3

12. 12 Powerset Given a set S, the power set of S is the set of all subsets of the set S. The power set is denoted by P(S). Let S={a,b,c} P(S) = { {}, S, {a},{b},{c}, {a,b},{a,c},{b,c}}

13. 13 Ordered n-tuple The ordered n-tuple (a 1,a 2,a 3,…a n ) is the ordered collection that has a 1 as its first element, a 2, as its second element,…, and a n as its n th element.

14. 14 Cartesian Product of A and B Let A and B be sets. The Cartesian Product of A and B, denoted by AxB, is the set of all ordered pairs (a,b) where and

15. 15 RxR R R (3,4)

16. 16 Problems from the text Pages 85-86 1-25 odd Homework will not be collected. However, you should do enough problems to feel comfortable with the concepts. For these sections the following problems are suggested.

17. 17 finished