## Discrete mathematics: mathematical reasoning and proof with puzzles, patterns, and gamesDid you know that games and puzzles have given birth to many of today's deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley's Introduction to Discrete Mathematics, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way. Online applications help improve your mathematical reasoning. Highly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. Explore More icons in the text direct you to online activities at www.wiley.com/college/ensley. Improve your grade with the Student Solutions Manual. A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text. |

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adjacency matrix algorithm answer arithmetic arrow diagram binary relation binary sequences binary tree Boolean algebra cards checked closed formula codomain column conclude contrapositive counterexample defined definition described digits divisible domain elements entry equation equivalent Eulerian Eulerian circuit exactly Example F F F F T F false formal function give given graph G Hamiltonian cycle Hank Hence integer inverse Karnaugh map length logic mathematical mathematical induction means natural number negation node notation one-to-one ordered list outcomes pigeonhole principle planar graph player positive integer possible Practice Problem predicate prime number Prob(E probability proof by contradiction properties Proposition prove puzzle rational number real numbers recurrence relation recursive reflexive represent result shown in Figure simple Solutions to Practice spanning tree statement P(m subset subtree Theorem transitive true truth table vertex vertices walk write