Discrete Mathematics: Elementary and Beyond

Discrete Mathematics: Elementary and Beyond L. Lovász J. Pelikán K. Vesztergombi Springer ...

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Preface For most students, the first and often only course in college mathematics is calculus. It is true that calculus is the s ...

vi Preface The aim of this book is not to cover “discrete mathematics” in depth (it should be clear from the description above t ...

Contents ...

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14 Finite Geometries, Codes, 1 Let’s Count! Preface v 1.1 AParty 1.2 Sets and the Like........................ 1.3 The Number o ...

1 Let’s Count! 1.1 AParty Alice invites six guests to her birthday party: Bob, Carl, Diane, Eve, Frank, and George. When they ar ...

2 1. Let’s Count! sits in the first chair, we can put any of the remaining 5 guests in the second chair; if Carl sits in the fir ...

1.1 A Party 3 only once, but 5· 4 · 3 · 2 ·1 times. So the number ofdifferenttickets is only 90 · 89 · 88 · 87 · 86 5 · 4 · 3 · ...

4 1. Let’s Count! “Yes, I think we have to agree on what the question really means,” adds Carl. “If we include in it who plays w ...

1.2 Sets and the Like 5 byZ+; the set of positive integers, denoted byN. Theempty set, the set with no elements, is another impo ...

6 1. Let’s Count! The notationA⊂Bmeans thatAis a subset ofBbut not all ofB.Inthe chain above, we could replace the⊆signs by⊂. If ...

1.2 Sets and the Like 7 CB A C B A FIGURE 1.1. The Venn diagram of three sets, and the sets on both sides of (1.1). Now, where a ...

8 1. Let’s Count! We get this simply by interchanging “union” and “intersection” in (1.1). (This identity can be proved just lik ...

1.3 The Number of Subsets 9 1.2.13We form the union of two sets. We know that one of them hasnelements and the other hasmelement ...

10 1. Let’s Count! It is not difficult to see that this is always the answer. Suppose you have to select a subset of a setAwithn ...