By K. Ribnikov

ISBN-10: 5030006109

ISBN-13: 9785030006109

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**Additional info for Analisis Combinatorio**

**Example text**

First, you have to figure out that the proposition is false. ) If a statement is false, you know why: you’ve found a particular case in which it is untrue, also known as a counterexample. So that’s all you have to do . . state that counterexample. 14 1. 8 (of a counterexample). Proposition: If n is even, then 2n − 5 is also even. This proposition is false, because 4 is an even number but 2 · 4 − 5 = 8 − 5 = 3 is odd and thus not even. An excellent reference for learning about proof techniques and proof writing is Book of Proof by Richard Hammack.

N) are members of the set denoted A × B × · · · × N, called the Cartesian product of the sets A, B, . . , N. The product principle. The number of elements in the Cartesian product of a finite number of finite sets A × B × · · ·× N is the product of their sizes |A| · |B| · · · · · |N|. 2, where we might consider |A| = 6 and |B| = 3. The same Cartesian product can be grouped as |B| copies of A, or as |A| copies of B. The product principle can also be formulated as making a collection of decisions or as putting choices in slots.

For example, instead of counting pets in a shelter, one could count paws and divide by four. ) Sometimes we will let one set stand in for another set in our attempts to count. This will work as long as we know how the sizes of the sets in question are related to each other. Here is another example that uses the product principle. 2. The Restaurant Quatre-Etoile offers prix fixe meals only. (That means you pay a fixed amount and get a k-course meal, where k usually varies between three and five.

### Analisis Combinatorio by K. Ribnikov

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