The Nature of Mathematics, 12th Edition
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Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
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Section 2.5: Review for Chapter 2

Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 2.

And [2.2]
Associative property for union and intersection [2.3]
Belongs to [2.1]
Cardinal number [2.1]
Cardinality [2.1]
Cartesian product [2.4]
Circular definition [2.1]
Complement [2.1]
Contained [2.1]
Countable set [2.4]
Countably infinite [2.4]
Counting number [2.1]
De Morgan's laws [2.3]
Description method [2.1]
Disjoint [2.1]
Element [2.1]
Empty set [2.1]
Equal sets [2.1]
Equivalent sets [2.1]
Finite set [2.4]
Fundamental Counting Principle [2.4]
Infinite set [2.4]
Integer [2.1]
Intersection [2.2]
Member [2.1]
Natural number [2.1]
One-to-one correspondence [2.4]
Or [2.2]
Proof by contradiction [2.4]
Proper subset [2.4]
Rational number [2.1]
Roster method [2.1]
Set [2.1]
Set-builder notation [2.1]
Set theory [2.1]
Subset [2.1]
Uncountable set [2.4]
Uncountably infinite [2.4]
Universal set [2.1]
Union [2.2]
Venn diagram [2.1]
Well-defined set [2.1]
Whole number [2.1]

If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).


Can you explain each of these important ideas in your own words?
Denoting Sets [2.1]
Sets of Numbers [2.1]
Universal and Empty Sets [2.1]
Equal and Equivalent Sets [2.1]
Venn Diagrams [2.1]
Operations with sets [2.1, 2.2, 2.3]
Cardinality of unions and intersections. {2.2]
De Morgan's laws [2.3]
Survey problems [2.3]
One-to-one correspondence [2.4]
Fundamental counting principle [2.4]

Next, make sure you understand the types of problems in Chapter 2.


Tell whether a set is well defined. [2.1]
Specify sets by roster and by description. [2.1]
Understand and use set-builder notation. [2.1]
Draw Venn diagrams showing subsets, equal sets, or disjoint sets. [2.1]
Distinguish between equal and equivalent sets, and find the cardinality of a given set. [2.1]
Distinguish the symbols for subset, proper subset, and element. [2.1]
Find the complement of a set [2.1, 2.2]
Find the union of two sets. [2.2]
Find the intersection of two sets. [2.2]
Recognize and draw the Venn diagrams for union, intersection, and complement. [2.2]
Solve survey problems involving two sets. [2.2]
Perform mixed operations using union, intersection, and complement [2.3]
Draw Venn diagrams for mixed operations using union, intersection, and complement. [2.3]
Draw Venn diagrams using three or more sets. [2.3]
Prove or disprove set statements using Venn diagrams. [2.3]
Solve survey problems involving three or more sets. [2.3]
Find the Cartesian product of two sets, and determine its cardinality. [2.4]
Find the cardinality of a given set. [2.4]
Determine whether sets have the same cardinality by placing them in a one-to-one
correspondence. [2.4]
Classify a given set at finite or infinite. [2.4]
Show that a given set has cardinality aleph null. [2.4]
Show that a given set is infinite. [2.4]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 2 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the book or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.