In this chapter, we study the structure of simple and compound statement through various logical connectives and different type of combination of statements.

Usually mathematical theorems are stated in the form of an implication p --> q or equivalence. Here P is called the Premises or hypothesis and q is called conclusion.

Aft.er going through this unit you should be able to learn the principle of Mathematical induction and establish some of the results involving a positive integer n.

This principle will assist us in establishing the formulae and also other applications of this principle will demonstrate its versatile nature in combinatorial mathematics.

After going through this unit you should able to define a recurrence relation with examples and setup recurrence relations also to write recurrences for divide and conquer algorithms.

The number C(n, r) are called Binomial Coefficients because they appear in the expansion of the binomial x + y raised to a power. This interplay between numbers that arise in counting problems. For example, in analyzing a problem involving counting we may derive some algebraic relation.

After going through this unit we can define and construct generating functions for sequences arising in various types of combination problems. Also we use generating functions to find the number of integer solution to linear equations. We solve recurrence relation using generating functions.

This section deals with the study of concept of binary relation and give you several geometric, computer and algebraic method of representations. Relationship between number, people, sets and any other entities can be formulated in the idea of the binary relation. In this section you will also learn the different properties that a binary relation can posess.

Through this unit we discuss about matrix digraphs relation along with transitive closure. Also of interest in how the relation matrix is used in the study of Graph theory.

In this section we learn more advanced feature on the relation like partial ordered sets and Lattices. These structures are useful in set theory, algebra, sorting and searching.

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