# Important Syllabus Discrete Structures and Theory of Logics AKTU Btech

The Discrete Structures and Theory of Logics course includes key ideas in computer science and mathematics, including logic, set theory, combinatorics, and graph theory. This blog presents a high-level summary of the program, highlighting its use in computational and logical contexts.

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Important Questions For Discrete Structures and Theory of Logics:
*Unit-01     *Unit-02
*Unit-03    *Unit-04
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 ```

## UNIT – 1: SETS, FUNCTIONS & NATURAL NUMBERS

• Set Theory:
• Introduction,
• Combination of sets,
• Multisets; Ordered pairs.
• Proofs of some general identities on sets.
• Relations:
• Definition,
• Operations on relations,
• Properties of relations,
• Composite Relations,
• Equality of relations,
• Recursive definition of relation,
• Order of relations.
• Functions:
• Definition,
• Classification of functions,
• Operations on functions,
• Recursively defined functions.
• Growth of Functions.
• Natural Numbers:
• Introduction,
• Mathematical Induction,
• Variants of Induction,
• Induction with Nonzero Base cases.
• Proof Methods, Proof by counter – example,

## UNIT – 2 : ALGEBRAIC STRUCTURES

• Definition, Groups, Subgroups and order,
• Cyclic Groups, Cosets, Lagrange’s theorem,
• Normal Subgroups, Permutation and Symmetric groups,
• Group Homomorphisms,
• Definition and elementary properties of Rings and Fields.

## UNIT – 3 : LATTICES & BOOLEAN ALGEBRA

• Lattices: Definition, Properties of lattices – Bounded, Complemented, Modular and Complete lattice.
• Boolean Algebra: Introduction, Axioms and Theorems of Boolean algebra, Algebraic manipulation of Boolean expressions.
• Simplification of Boolean Functions, Karnaugh maps, Logic gates,
• Digital circuits and Boolean algebra.

## UNIT – 4: PROPOSITIONAL & PREDICATE LOGIC

• Propositional Logic: Proposition,
• well formed formula, Truth tables,
• Algebra of proposition,
• Theory of Inference.
• Predicate Logic: First order predicate,
• well formed formula of predicate, quantifiers,
• Inference theory of predicate logic.

## UNIT – 5: TREES, GRAPHS & COMBINATORICS

• Trees:
• Definition,
• Binary tree,
• Binary tree traversal,
• Binary search tree.
• Graphs:
• Definition and terminology,
• Representation of graphs,
• Multigraphs,
• Bipartite graphs,
• Planar graphs,
• Isomorphism and Homeomorphism of graphs,
• Euler and Hamiltonian paths,
• Graph coloring,
• Recurrence Relation & Generating function:
• Recursive definition of functions,
• Recursive algorithms, Method of solving recurrences.
• Combinatorics:
• Introduction,
• Counting Techniques,
• Pigeonhole Principle.