ELEMENTS OF DISCRETE MATHEMATICS

1.1 Indian Logic

1.1.1 Origins, 1.1.2 The schools Vaisheshika, 1.1.3 Catuskoti, 1.1.4 Nyaya, 1.1.5 Jain logic, 1.1.6 Buddhist logic, 1.1.7 Navya-Nyaya, 1.1.8 Influence of Indian logic on modern logic, 1.1.9 Boolean Logic and Indian Thoughts.

1.2 Relations

1.2.1 Binary, Inverse, Composite and Equivalence relation, 1.2.2 Equivalence classes and its properties, 1.2.3 Partition of a set, 1.2.4 Partial order relation, 1.2.5 Partially ordered and Totally ordered sets, 1.2.6 Hasse diagram.

1.3 Lattices

1.3.1 Definition and examples, 1.3.2 Dual, bounded, distributive and complemented lattices.

Unit-II

2.1 Boolean Algebra

2.1.1 Definition and properties, 2.1.2 Switching circuits and its applications, 2.1.3 Logic gates and circuits. 2.2 Boolean functions

2.2.1 Disjunctive and conjunctive normal forms, 2.2.2 Bool's expansion theorem, 2.3 Minimize the Boolean function using Karnaugh Map.

Unit-III

Graphs :

3.1 Definition and types of graphs, 3.2 Subgraphs, 3.3 Walk, path and circuit, 3.4 Connected and disconnected graphs, 3.5 Euler graph, 3.6 Hamiltonian path and circuit, 3.7 Dijkstra's Algorithm for shortest paths in weighted graph.

Unit-IV

Tree :

4.1 Trees and its properties, 4.2 Rooted, Binary and Spanning tree, 4.3 Rank and nullity of a graph, 4.4 Kruskal's and Prim's Algorithm, 4.5 Cut-set and its properties,