By Mark Dugopolski

**Algebra for college kids, 5e **is a part of the most recent choices within the profitable Dugopolski sequence in arithmetic. The author’s target is to provide an explanation for mathematical thoughts to scholars in a language they could comprehend. during this publication, scholars and school will locate brief, specific motives of phrases and ideas written in comprehensible language. the writer makes use of concrete analogies to narrate math to daily reviews. for instance, whilst the writer introduces the Commutative estate of Addition, he makes use of a concrete analogy that “the fee of a hamburger plus a Coke is equal to a Coke plus a hamburger”. Given the significance of examples inside of a math e-book, the writer has paid shut awareness to an important info for fixing the given subject. Dugopolski encompasses a double cross-referencing process among the examples and workout units, so irrespective of which one the scholars commence with, they'll see the relationship to the opposite. ultimately, the writer reveals it vital not to merely offer caliber, but additionally a superb volume of routines and purposes. The Dugopolski sequence is understood for delivering scholars and school with the main volume and caliber of workouts compared to the other developmental math sequence out there. In finishing this revision, Dugopolski feels he has built the clearest and so much concise developmental math sequence out there, and he has performed so with no comprising the basic info each scholar must develop into profitable in destiny arithmetic classes.

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**Example text**

4, 5, 6, 7, . ͖ 9 92. Cooperative learning Work with a small group to answer the following questions. If A ʕ B and B ʕ A, then what can you conclude about A and B? If (A ʜ B) ʕ (A ʝ B), then what can you conclude about A and B? 87. ͕6, 8, 10, 12, . . , 82͖ 88. ͕9, 11, 13, 15, . . , 51͖ 93. Discussion U6V Applications What is wrong with each statement? Explain. Solve each problem. See Example 7. 89. In a class of 30 students all of them are either female or smokers, while only 5 are female and smokers.

3 sure exercise. 4 you will see how an algebraic expression can determine your target heart rate for beneficial exercise. In this section we will learn the basic terms and facts about sets. U1V Set Notation A set is a collection of objects. At home you may have a set of dishes and a set of steak knives. In algebra, we generally discuss sets of numbers. For example, we refer to the numbers 1, 2, 3, 4, 5, and so on as the set of counting numbers or natural numbers. Of course, these are the numbers that we use for counting.

If A is not a subset of B, we write A B. 4 CAUTION To claim that A B, there must be an element of A that does not belong to B. For example, ͕1, 2͖ ͕2, 3, 4͖ because 1 is a member of the first set but not of the second. Is the empty set л a subset of ͕2, 3, 4͖? If we say that л is not a subset of ͕2, 3, 4͖, then there must be an element of л that does not belong to ͕2, 3, 4͖. But that cannot happen because л is empty. So л is a subset of ͕2, 3, 4͖. In fact, by the same reasoning, the empty set is a subset of every set.