Discrete Mathematics with ApplicationsDesigned to provide a strong mathematics background for computer science, engineering, and mathematics students. Topics in the text are drawn from logic, Boolean algebra, combinatorics, automata, and graph theory. A chapter on automata theory and formal languages is included along with programming notes using Pascal language constructions to show how programming and mathematics are related. Logic is introduced briefly in chapter one and then expanded upon in chapter four. |
Contents
INTRODUCTION TO SETS ALGORITHMS AND LOGIC | 1 |
CHAPTER | 10 |
CHAPTER 7 | 32 |
Copyright | |
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a₁ A₂ adjacency matrix algorithm antisymmetric Assume B₁ bijective function binary numbers binary operation binary relation binary tree bit strings Boolean algebra laws Boolean expression Boolean function called Card(A computer program connected corresponding defined definition digits digraph edges Eulerian tour Exercise Set factor false Find the number finite set gcd(a given grammar graph G Hamiltonian cycle Hence input integer Karnaugh map logic network loop mathematical induction method minimal sum minterms Morgan's law multigraph negation notation obtain output partial order Pascal path positive integer Pr(A Pr(AB Pr(B Pr(E PRACTICE PROBLEM prime proof propositional logic quantifiers real numbers recurrence relation reflexive sample space Section sequence Solution spanning tree standard sum statement subgraph subset sum of products Suppose symbol symmetric tautology Theorem transitive closure true truth table truth values v₁ variables Verify vertex vertices write x'yz