Logic is the discipline that deals with the methods of reasoning. On an elementary level, logic provides rules and techniques to determine whether a given statement (argumep') is valid. Logical reasoning is used in mathematics to prove theorems, and in computer science to verify the covertness of programs. Logic has its applications in various other fields such as natural science, social science a ......

In this unit concepts like equivalence of WFFs, tautological implication, duality of WFF, two important normal forms namely disjunctive and conjunctive forms and finally inference process given some set of premises are discussed in various sections, in detail with several examples.

Set theory is being used in various fields of science and engineering. The main purpose of set theory is to study the importance of discrete objects and relationships among them. This unit deals wi th different types of sets, set operations and principle of induction.

In this unit we discussed basic methods of counting namely Permutation and Combination. Several illush'ations are discussed for better understanding of the usage of permutation or combination. Later, Pigeonhole Principle and its extension are also stated aud several examples solved.

Relation is a basic concept ii1 day to day life and Mathematics. A relation shows an association of objects of a set with objects of other sets (or the same set). The essence of relation is these associations. A collection of these individual associations is a relation. To represent these individual associations, a set of "related" objects, can be used. The order of the objects must also be taken ......

A recurrence relation is an equation that recursively defines a sequence: each term of the sequence is defined as a function of the preceding terms. The term difference equation sometimes refers to a specific type of recurrence relation. Note however that "difference equation" is frequently used to refer to any recurrence relation. Some simply defined recurrence relations can have very complex (ch ......

A generating function is a formal power series in one indeterminate, whose coefficients encode information about a sequence of numbers that is indexed by the natural numbers. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general linear recurrence problem.

A relation is mainly a correspondence between the members of two sets, associating members of the first set with those of the second. It is possible that a give relation associates with any member of the first set several different members of the second set. It is possible that some elements of the first set are not associated with any from the second. A special type of relation is that which asso ......

In this unit an important concept called graph is introduced. Some interesting applications are discussed here. Diagrammatic representation of a graph, types of graphs and matrix representation of graphs also are discussed.

The unit begins with isomorphism of graphs. Concepts like walks, paths, circuits and Euler graphs are discussed with ample examples. Connectedness is an important concept useful for many applications. This idea is discussed in length here also giving the matrix structure of disconnected graphs. Special circuits and paths called Hamiltonian circuits and Hamiltonian paths and a very important proble ......

In this unit, we discuss planar graphs. The question of planarity is of great significance in many practical situations, such as printed circuit board (to determine if a single layer is sufficient to make all connections), proper coloring of a graph and the partitioning of vertices. Partitioning of vertices has many practical applications such as coding theory, state reduction of sequential machin ......

In this unit we describe a graph structure called tree and state some interesting properties of trees. Spanning tree is important structure with many applications. Spanning tree is discussed and two algorithms for finding minimum weight spanning tree are discussed in length. Searching graphs is another important procedure in computer science. Two search procedures depth first and breadth first are ......

Semigroups are the simplest algebraic structures which satisfy the properties of closure and associativity, They are very important in the theory of sequential machines, formal languages and in certain applications relating to computer arithmetic such as multiplication. A monoid in addition to being a semigroup, also satisfies the identity property. Monoids are used in a number of applications, bu ......

Application of subgroups is in the construction of computer modules which perform group operations. Such modules are constructed by joining various subgroup modules that do operations in subgroups. Every subset of a group need not be a subgroup. To find those subsets which can qualify to become subgroups is an interesting problem. An important relationship exists between the subgroups and the grou ......

The concept of isomorphism shows that two algebraic systems which are isomorphic to one another are structurally indistinguishable and that the results of operations in one system can be obtained from those of the other by simply relabeling the names of the elements and symbols for operations. This concept has useful applications in the sense that the results of one system permit an identical inte ......

Error-detection and correction techniques have become increasingly important in the design of computer systems. Most systems contain telephone and communication lines which cause transmitted messages to be conupted by the presence of noise. Peripheral equipment associated with such systems is by far the most unreliable component of these systems and both error detection and error correction are fr ......

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