# sets theory | Mathematical Logic | Matrices |Graphs theory | BCA-I | SEM-II

In this article **sets theory** we give the detailed **syllabus for BCA Part I** Mathematical Foundations For Computer Applications, sets operations and all points related easy notes.

## SETS Theory:

**1.1 Introduction.****1.2 Methods of describing of a set: Tabular form, Set builder form. ****1.3 Finite set, Infinite set, Empty set, Subset, Universal set, Equal sets, ****Disjoint sets, Complementary set.**

**Above 3 points Set Theory 1st Article**

**1.4 Operation on Sets: Union of sets, Intersection of sets, Difference of sets, ****Examples. ****1.5 De Morgan’s Laws (without proof).**

**Above 2 points Set Theory 2nd Article**

**1.6 Venn diagram, Examples. ****1.7 Cartesian product of two sets, Examples.**

**Above 2 points Set Theory 3rd Article**

**1.8 Idempotent laws, Identity laws, Commutative Laws, Associative laws, ****Distributive laws, Inverse laws, Involution laws. ****1.9 Duality.****1.10 Relations and Functions: Introduction, Operations on Functions,****Injective, surjective and bijective functions**

**Above 3 points Set Theory Last Article**

#### II Logic:

2.1 Introduction.

2.2 Definition: Statement (Proposition).

2.3 Types of Statements: Simple and compound statements.

2.4 Truth values of a statement.

2.5 Truth Tables and construction of truth tables.

2.6 Logical Operations: Negation, Conjunction, Disjunction, Implication,

Double Implication.

2.7 Equivalence of Logical statements.

2.8 Converse, Inverse and Contra positive.

2.9 Statement forms: Tautology, Contradiction, and Contingency.

2.10 Duality, Laws of logic: Idempotent laws, Commutative laws,

Associative laws, Identity laws,

Involution laws, Distributive laws, Complement laws, De Morgan’s laws.

2.11 Argument: Valid and Invalid arguments.

2.12 Examples based on above.

#### III Matrices:

3.1 Introduction.

3.2 Types of matrices: Row matrix, Column matrix, Null matrix, Unit matrix,

Square Matrix, Diagonal matrix, Scalar matrix, Symmetric matrix, Skew –

symmetric matrix, Transpose of a matrix,

3.3 Definition of Determinants of order 2nd & 3rd and their expansions

3.4 Singular and Non-Singular Matrices

3.5 Algebra of Matrices: Equality of matrices, Scalar Multiplication of

matrix, Addition of matrices, Subtraction of matrices, Multiplication of

matrices.

3.6 Elementary Row & Column Transformations

3.7 Inverse of Matrix (Using Elementary Transformations)

3.8 Examples based on above.

#### IV Graphs:

4.1 Introduction

4.2 Simple graph, Multi graph, Pseudo Graph

4.3 Digraph

4.4 Weighted Graph

4.5 Degree of Vertex, Isolated Vertex, Pendant Vertex.

4.6 Walk, Path, Cycle.

4.7 Types of Graph: Complete, Regular, Bi-Partite, Complete Bi-partite.

4.8 Matrix Representation of Graph: Adjacency and Incidence Matrix.

4.9 Operation on Graph: Union, Intersection, Complement.

4.10 Examples based on above