Algebra • Definition: − An Algebra is characterized by specifying the following three components. Discrete Mathematics, Spring 2009 1. a set called the carrier of the algebra, 2. operators defined on the carrier, and 3. (distinguished elements of the carrier, called the constants of the algebra.) ....

**Fundamental Approach to Discrete Mathematics by D.P. Acharjya full eBook**

CHAPTER 1 Counting 1 1.1 Basic Counting 1 The Sum Principle 1 Abstraction 3 Summing Consecutive Integers 3 The Product Principle 4 Two-Element Subsets 6 Important Concepts, Formulas, and Theorems 7 Problems 8 1.2 Counting Lists, Permutations, and Subsets 10 Using the Sum and Product Principles 10 Lists and Fu....

1 The Foundations: Logic and Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Propositional Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Applications of Propositional Logic . . . . . . . . . . . . . . . . . . . . . . . . . . ....

SYLLABUS Unit-I Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs,Set Identities. Relations: Definition, Operations on relations, Properties of relations, Composite Relations, Equality of relations, Order of relations. Functions: Definition, Classification of functions,Operations on functions, Recursively defined function....

Set : Any well defined collection of distinct objects is called a set. The objects in a set can be numbers, people, letters, rivers, countries etc. The objects in a set are called the elements or members of the set. Examples : 1. The set of numbers 4, 6, 8, 10. 2. The set of letters a, e, i, o, u.