Discrete Mathematics for Computer Science by Gary Haggard, John Schlipf, Sue Whitesides PDF

By Gary Haggard, John Schlipf, Sue Whitesides

Progressively more laptop scientists from varied components are utilizing discrete mathematical buildings to give an explanation for techniques and difficulties. in response to their instructing reviews, the authors supply an available textual content that emphasizes the basics of discrete arithmetic and its complex themes. this article indicates the best way to convey distinct rules in transparent mathematical language. scholars become aware of the significance of discrete arithmetic in describing laptop technology constructions and challenge fixing. additionally they find out how studying discrete arithmetic can assist them advance very important reasoning abilities that may stay priceless all through their careers.

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Example text

Let A be the set of black cards and B the set of 3's. The example asks for the size of I A U B I. Clearly, IA I = 26, and I B I = 4. The problem is that two of the 3's are also black. In this case, I A n B I # 0. The count I A I + I B I overcounts by IA n B I. The answer is IAUB = IAI+IBI-IAnBI =26+4-2=28 U The card problem in Example 6 is a special example of the Principle of InclusionExclusion that we prove in more generality next. Theorem 2. (Principle of Inclusion-Exclusion for Two Sets) sets.

Clearly, IA I = 26, and I B I = 4. The problem is that two of the 3's are also black. In this case, I A n B I # 0. The count I A I + I B I overcounts by IA n B I. The answer is IAUB = IAI+IBI-IAnBI =26+4-2=28 U The card problem in Example 6 is a special example of the Principle of InclusionExclusion that we prove in more generality next. Theorem 2. (Principle of Inclusion-Exclusion for Two Sets) sets. Then, IAUBI = IAI+IBI - IAnBI Let A and B be finite The Principle of Inclusion-Exclusion 37 The number of elements in the union of two finite sets is the sum of the number of elements in each of the sets minus the number of elements in their intersection.

In the process, all the elements of A n B have been counted twice, so subtract I A n B I to compensate.

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Discrete Mathematics for Computer Science by Gary Haggard, John Schlipf, Sue Whitesides


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