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.
Above 3 points Set Theory 1st Article
Above 2 points Set Theory 2nd Article
Above 2 points Set Theory 3rd Article
1.8 Idempotent laws, Identity laws, Commutative Laws, Associative laws,
Distributive laws, Inverse laws, Involution laws.
1.10 Relations and Functions: Introduction, Operations on Functions,
Injective, surjective and bijective functions
Above 3 points Set Theory Last Article
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,
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.
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
3.6 Elementary Row & Column Transformations
3.7 Inverse of Matrix (Using Elementary Transformations)
3.8 Examples based on above.
4.2 Simple graph, Multi graph, Pseudo Graph
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