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Section 2.2: Complements, Subsets, and Venn Diagrams
Practice HW from Mathematical Excursions Textbook (not to hand in) p. 71 # 1-49 odd In the section, we continue with our discussion of basic set concepts.
The Universal Set and Compliment of a Set
The universal set is the set U of all possible elements being considered for a particular problem. Example 1: Find an appropriate universal set for the elements Virginia, Texas, Virginia, and Ohio Solution: █ Definition: The compliment of set A is the set of all elements in the universal set U that are not in the set A.
Notation for Compliment: Given a set A , the compliment is given by A .
Example 2: Find the compliment of the following sets given that the universal set is U { 0 , 1 ,2,3,4,5,6,7,8, 9}. a. {0,1,4,5,6} b. {^ x^ | x ^6 and x W } c. {}or d. U
Example 4: Given the sets U^ {a,e,i,o,u}, W^ {a,i,o,u}, X^ {a,u}, and Y^ {^ e }, determine whether the following is true or false. a. X^ W b. X^ W
c. Y W
d. Y^ U e. Y
Listing the Subsets of a Set
Fact: A subset containing n elements contains 2 n subsets. Example 5: List the number and all of the subsets of the set {dog,cat} Solution: █ Example 6: List the number and all of the subsets of the set {1,3,5,7}
Solution: █
