SYLLABUS
Course Code Course Name
Category
L T P C
   MA25C08  DISCRETE MATHEMATICS
Unit – 1: Set Theory, Relations and Functions: Set theory – inductive
definition of sets and proof by induction – Peano postulates – Relations
– equivalence relations and partitions. Functions – Type of functions:
Injective, surjective and bijective functions – Composition of functions –
Inverse functions – Permutation functions – Recurrence relations – Solving
linear recurrence relations.
Activities: Create and present Venn diagrams to illustrate union,
intersection, Categorize real-world mappings such as student-to-email ID,
username-to-password, as injective, surjective, or bijective using role-play
or sorting tasks.
Unit – 2: Logic: Propositions – Logical operators – Normal forms –
Rules of inference – Consistency and inconsistency – Propositional logic
– Proofs – Predicates – Quantifiers – Universe of discourse – Logical
equivalences and implications for quantified statements – Rules of
specification and generalization – Validity of arguments.
Activities: Conduct a truth table building competition for compound
propositions using logical operators.
Unit – 3: Boolean Algebra and Lattice Theory: Partial ordering –
Posets – Lattices as Posets – Properties of lattices – Lattices as algebraic
systems – Sub lattices – Direct product and homomorphism – Some special
lattices – Boolean algebra – Sub Boolean Algebra – Boolean
Homomorphism.
Activities: Draw Hasse diagrams for lattices from a given set and
identify sublattices and lattice operations.
Unit – 4: Graph Theory: Graphs – Types of graphs – Matrix
representation of graphs – Graph isomorphism – Walk – Path – Cycles –
Eulerian graphs – Hamiltonian graphs – Planar graphs – Euler formula –
Shortest path algorithm: Dijkstra’s algorithm.
Activities: Implement Dijkstra’s algorithm to find the shortest path in
a weighted AI decision graph.
Weightage: Continuous Assessment: 40%, End Semester Examinations: 60%
Assessment Methodology: Assignment (20%), Solution to
application-oriented problems using software (20%), Solving Competitive
Examination questions (20%), Internal Examinations (40%).