## Discrete MathematicsThis book contains a judicious mix of concepts and solved examples that make it ideal for the beginners taking the Discrete Mathematics course. Features Exhaustive coverage of Set Theory. Comprehensive coverage of Graph Theory and Combinatorics. Excellent discussion of Group theory applications-Coding. Detailed explanation of the solution procedure of the worked examples. Pedagogy includes 341 solved examples 566 short answer questions 556 descriptive questions Over 500 figures and tables |

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### Contents

Preface | viii |

SET THEORY | 51 |

NUMBER THEORY | 156 |

FUNCTIONS | 182 |

GROUP THEORY | 232 |

COMBINATORICS | 314 |

GRAPH THEORY | 366 |

FORMAL LANGUAGES AND AUTOMATA THEORY | 448 |

Finitestate Machine | 461 |

Exercise 8B | 482 |

Worked Examples 8C | 497 |

Exercise 8C | 513 |

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### Common terms and phrases

a v b accepted algebraic system binary operation binary tree Boolean algebra called cell code word column commutative complement congruence corresponding coset decoding defined Definition denoted digits divisors equivalence relation Eulerian circuit example F F F F T F Find finite gcd(a given in Fig grammar Hamiltonian circuit Hasse diagram Hence homomorphism idempotent identity element input integers inverse isomorphic lattice matrix minterms modulo monoid Morgan's law multiple number of edges one-to-one output p a q p v q path permutations poset positive integers primitive recursive primitive recursive function Proof prove real numbers recurrence relation recursive function represented semigroup Similarly solution spanning tree statement string subgraph subgroup of G subset symbol symmetric theorem transitive truth table Turing machine variables vertex vertices