By Mark Dugopolski

ISBN-10: 0073533521

ISBN-13: 9780073533520

Algebra for students, 4th version, is designed to supply scholars with the algebra heritage wanted for extra college-level arithmetic classes. The unifying subject matter of this article is the advance of the talents valuable for fixing equations and inequalities, by way of the appliance of these talents to fixing utilized difficulties. this article includes 2 chapters, Polynomial & Rational features, and Counting & chance, as well as these present in Dugopolski's Intermediate Algebra.

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**Additional info for Algebra for College Students, 5th Edition **

**Sample text**

A) List all possible subsets of ͕1, 2͖. How many are there? b) List all possible subsets of ͕1, 2, 3͖. How many are there? c) Guess how many subsets there are of ͕1, 2, 3, 4͖. Verify your guess by listing all the possible subsets. d) How many subsets are there for ͕1, 2, 3, . . , n͖? There are many different types of real numbers. To understand better the set of real numbers, we will study some of the subsets of numbers that make up this set. U1V The Rational Numbers U2V Graphing on the Number Line U3V The Irrational Numbers U4V The Real Numbers U5V Intervals of Real Numbers U1V The Rational Numbers We use the letter N to name the set of counting or natural numbers.

C) Graph (Ϫ1, 2) and [0, ϱ) as in Fig. 27. The union of these intervals consists of the real numbers greater than Ϫ1, which is written as (Ϫ1, ϱ). d) Examining the graphs in Fig. 27, we see that the real numbers between 0 and 2 belong to both intervals. Note that 0 also belongs to both intervals but 2 does not. So the intersection is [0, 2). 27 Now do Exercises 85–96 Warm-Ups True or false? Explain your answer. ▼ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. The number is a rational number. The set of rational numbers is a subset of the set of real numbers.

A ʜ B ϭ ͕1, 2, 3, 4, 5, 6, 8͖ Now examine A ʜ B and C to find the elements that belong to both sets: A ʜ B ϭ ͕1, 2, 3, 4, 5, 6, 8͖ C ϭ ͕4, 5, 7͖ The only numbers that are members of A ʜ B and C are 4 and 5. Thus, (A ʜ B) ʝ C ϭ ͕4, 5͖. 5 B A 1, 3 2 4 6, 8 5 Every possibility for membership in three sets is shown in the Venn diagram in Fig. 5. 6 shows the numbers from the three sets of Example 6 in the appropriate regions of this diagram. Since no number belongs to all three sets, there is no number in the center region of Fig.

### Algebra for College Students, 5th Edition by Mark Dugopolski

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