This third edition offers an introduction to discrete mathematics, covering relations, induction, counting techniques, logic and graphs. More advanced topics of Boolean algebra and permutation groups are included, and there are numerous examples to reinforce the material.
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INDUCTION AND RECURSION 164
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acyclic digraph algorithm binary tree Boolean algebra Boolean expression Boolean function Calculate called colors compound proposition compute connected Consider contains cosets countable cycle deﬁned digraph disjoint elements equivalence classes equivalence relation Euler path exactly EXAMPLE false ﬁnd ﬁnite set ﬁrst ﬁve function f give given graph G graph in Figure group G Hasse diagram Hence homomorphism inﬁnite input integers inverse isomorphic logically equivalent loop invariant maps marbles Mathematical Induction matrix minimum spanning tree minterm multiple nonempty notation obtain orbits parallel edges partial order partition paths of length permutation poset predicate Principle probability proof Prove random variable real numbers recursive deﬁnition reﬂexive Repeat Exercise rooted tree rule satisﬁes semigroup Show smallest sorted labeling subgroup subset Suppose tautology Theorem tion tossed true truth table truth values vertex vertex sequence vertices weight write