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

By Mark Dugopolski

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

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**Sample text**

So Ϳ a Ϳ is greater than or equal to zero for any number a. Two numbers that are located on opposite sides of zero and have the same absolute value are called opposites of each other. The opposite of zero is zero. Every number has a unique opposite. The numbers 9 and Ϫ9 are opposites of one another. ” If a is positive, Ϫa is negative. If a is negative, Ϫa is positive. Opposites have the following property. Opposite of an Opposite For any number a, Ϫ(Ϫa) ϭ a. E X A M P L E 2 Opposite of an opposite Evaluate.

3 E X A M P L E 4 A Venn diagram can be used to illustrate the result of Example 3(a). Since 2 and 3 belong to both A and B, they are placed in the overlapping region of Fig. 3. Since 0 is in A but not in B, it is placed inside the circle for A but outside B. Likewise 7 is placed inside B but outside A. Membership and equality Let A ϭ ͕1, 2, 3, 5͖ and B ϭ ͕2, 3, 7, 8͖. Place one of the symbols ϭ, blank to make each statement correct. a) 5 _____ A ʜ B b) 5 _____ A ʝ B c) A ʜ B _____ ͕l, 2, 3, 5, 7, 8͖ d) A ʝ B _____ ͕2͖ , ʦ, or in the Solution a) 5 ʦ A ʜ B because 5 is a member of A.

Is not a member of is not a subset of not equal intersection A ϭ ͕x Ϳ x is a counting number͖ The set B has an infinite number of elements. The set of counting numbers less than 50 million is an infinite set. 1ʦAʝB 5. 3 ʦ A ʜ B 6. A ʝ B ϭ C CʕB 8. A ʕ B 9. com! > Practice Problems > NetTutor > Self-Tests > e-Professors > Videos Exercises U Study Tips V • Exercise sets are designed to increase gradually in difficulty. So start from the beginning and work lots of exercises. • Find a group of students to work with outside of class.