Equivalence Relation and equivalence class| Discrete mathematical structures By Infee Tripathi
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- เผยแพร่เมื่อ 27 ส.ค. 2024
- In this course of Discrete Mathematical structure we will serve all the topics asked in a LT Grade, GATE, UGC NET, KVS, NVS, DSSSB and any other TGT/PGT competitive examination in the easiest way.
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Clear Explanations
Practice Problems with Solutions
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In this series we are going to cover:
Set Theory: Sets, subsets, and set operations.
Set equality and set cardinality.
Universal sets and complements.
Venn diagrams. relation:- reflexive ,irreflexive symmetry, antisymmetry, Asymmetry, transitive, equivalence, inverse, complement etc
Graph Theory:
Basics of graphs, vertices, and edges.
Types of graphs (e.g., trees, bipartite graphs).
Graph isomorphism.
Graph traversal algorithms (e.g., depth-first search, breadth-first search).
Combinatorics:
Permutations and combinations.
Pigeonhole principle.
Relations and Functions:
Binary relations and equivalence relations.
Partial orders and lattices.
Functions, injections, and surjections.
Composition and inverse functions.
Logic: Propositional logic.
Predicate logic.
Logical equivalences and quantifiers.
Formal proofs and proof techniques.
Counting and Enumeration:
Combinatorial problems (e.g., permutations with restrictions, combinations with repetitions).
Recurrence Relations:
Set Algebra: Operations on sets, laws of set theory.
De Morgan's Laws.
Set partitions and power sets.
Combinatorial Graph Theory:
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