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