Set theory: Hasse diagram, relationships, circles Euler

Detailed solution control work in discrete mathematics.

Discrete mathematics - part of mathematics that studies discrete mathematical structures, such as graphs and statements in logic. In the context of the whole of mathematics Discrete mathematics is often identified with a finite mathematics - the direction of studying the structure of finite - finite graphs, finite groups, finite state machines. It is possible to identify some of the features are not inherent in the divisions, working with endless and continuous structures. For example, in the discrete directions are usually wider class of solvable problems, since in many cases a complete listing possible options, while sections, dealing with endless and continuous structures, for the solubility usually requires substantial restrictions on the conditions. In the same context, especially in discrete mathematics are important task of building a specific algorithms, and including effective in terms of computational complexity. Another feature of discrete mathematics - the impossibility of applying it to the extreme problems of analysis techniques, essentially using discrete structures inaccessible to the smoothness of the concept. In a broad sense, discrete mathematics can be considered as covered large parts of algebra, number theory, mathematical logic.

As part of the curriculum discrete mathematics is usually regarded as a set of sections associated with applications to computer science and computer engineering: the theory of functional systems, graph theory, automata theory, coding theory, combinatorics, integer programming.