Discrete Structures – CNS2300

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

2. Section 1.6 Sets

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

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. Set Builder Notation

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

9. Proper Subset True/False

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

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. IfS={a,b,c}then|S| = 3

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. Ordered n-tuple The ordered n-tuple(a1,a2,a3,…an)is the ordered collection that has a1as its first element, a2, as its second element,…, and anas its nth element.

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) whereand

15. RxR R (3,4) R

16. Problems from the text 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. Pages 85-86 1-25 odd

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