Titlebook: Discrete Mathematics with Graph Theory; Santosh Kumar Yadav Textbook 2023 The Author(s) 2023 Euclid’s Algorithm.Euclid’s Theorem.Congruenc

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Directed Graphs,h problems of traffic flow, it is necessary to know which roads in the network are one-way, and, in which direction the traffic is permitted. It is clear that, a graph of the network is not of much use in such a situation. We need in a graph, in which, each link has an assigned orientation - a ..

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Matching and Covering,its vertices in this way? If not, how can we be sure that this is indeed impossible? Somewhat surprisingly, this basic problem does not only lie at the heart of numerous applications, it also gives rise to some rather interesting graph theory.

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Jean-Baptiste Valsamis,Pierre LambertA set is a well defined collection of distinct objects, sets are of fundamental importance in mathematics. The very number systems that we studied in the preceding chapter were all discussed in terms of set of numbers.

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Pierre Lambert,Jean-Baptiste ValsamisAn important part of discrete mathematics is combinatorics which is used to solve counting problems without enumerating all possible cases. Combinatorics deals with counting the number of ways of arranging or choosing objects from a finite set according to certain specific rules or methods.

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J. J. Mecholsky,P. F. Becher,S. W. FreimanIn our daily life, we always experience a large number of attributes which are not precise. But human brain always processes such imprecise terms. If my doctor asks me “.”; I reply “.” Here the media of communication for information passing is not mathematical but something else which are not well modelled in any way.

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The Language of Sets,A set is a well defined collection of distinct objects, sets are of fundamental importance in mathematics. The very number systems that we studied in the preceding chapter were all discussed in terms of set of numbers.

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Functions,The concept of a function is so fundamental that plays an important role of a unifying thread to intertwines every branch of mathematical sciences. It is almost used is our daily life as well. When we compute our electricity bill or water bill, we use the concept of functions unknowingly.