Reflexive Relation with examples | Discrete Mathematics | GATECSE

In this video, we completely explain the Reflexive Relation — one of the six fundamental properties of relations in Discrete Mathematics. We cover the definition, notation, how to check the reflexive property using ordered pairs, matrix method, and digraph method, important theorems, tricky GATE-style questions, and step-by-step solved examples. If the Reflexive Relation has ever confused you — this lecture gives you complete, exam-ready clarity. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📌 TOPICS COVERED IN THIS VIDEO ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ ✔ Quick Recap — Properties of Relations Overview ✔ What is a Reflexive Relation? — Definition & Notation ✔ Formal Definition — (a,a) ∈ R for ALL a ∈ A ✔ How to CHECK if a Relation is Reflexive ✔ Reflexive Relation — Solved Examples (Simple to Complex) ✔ What is an Irreflexive Relation? ✔ Number of Reflexive Relations on a Set with n Elements ✔ Important Properties & Theorems on Reflexive Relations: ✔ Reflexive Closure of a Relation ✔ Reflexive Relation as building block — Partial Orders, Equivalence ✔ Tricky GATE-Style Questions on Reflexive Relations ✔ Solved GATE-Level & University Exam Practice Problems ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📂 SUBJECT WISE PLAYLIST ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🔗Data Structures: http://tinyurl.com/bwptf6f7 🔗Theory of Computation: http://tinyurl.com/5bhtzhtd 🔗Compiler Design: http://tinyurl.com/2p9wtykf 🔗Design and Analysis of Algorithms: http://tinyurl.com/ywk8uuzc 🔗Graph Theory: http://tinyurl.com/3e8mynaw 🔗Discrete Mathematics: http://tinyurl.com/y82r977y 🔗C Programming: http://tinyurl.com/2556mrmm 🔗 Operating System: https://tinyurl.com/ms7rxc46 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🎯 WHY THIS TOPIC MATTERS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📘 FOR GATE CSE: Reflexive Relation is a core property tested DIRECTLY in GATE CSE Discrete Mathematics every year. It is also the FIRST condition in both Equivalence Relations (Reflexive + Symmetric + Transitive) and Partial Order Relations (Reflexive + Antisymmetric + Transitive). Without mastering Reflexive, you cannot correctly answer questions on Equivalence, POSET, or Lattice Theory. This is foundational. 🎓 FOR SEMESTER & MFCS EXAMS: Reflexive Relation is among the first topics tested in Discrete Mathematics and MFCS university exams across VTU, AKTU, Anna University, Mumbai University, RTU, JNTU, and all major Indian universities. Definition-based, example-based, and matrix-based questions on Reflexive Relation appear in both internal and end-semester exams. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🧠 WHAT YOU WILL LEARN ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ After watching this video, you will be able to: → Define Reflexive Relation precisely using formal notation → Check if any given relation is Reflexive using all three methods → Distinguish between Reflexive, Irreflexive, and Neither → Count the number of Reflexive Relations on a set with n elements → State and apply all key theorems on Reflexive Relations → Find the Reflexive Closure of any given relation → Solve GATE and university exam tricky questions on Reflexive Relations → Use Reflexive as a building block for Equivalence & Partial Orders ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 🔎 RELATED SEARCHES ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ reflexive relation discrete mathematics | reflexive relation examples | how to check reflexive relation | reflexive vs irreflexive relation | number of reflexive relations formula | reflexive closure of a relation | reflexive relation matrix method | reflexive relation digraph | reflexive relation gate cse 2026 | properties of relations discrete mathematics ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 📢 STAY CONNECTED — THE GATEHUB ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Instagram:   / thegatehub   LinkedIn:   / thegatehub   Twitter:   / thegatehub   Contact/Collaboration: thegatehub2020@gmail.com Website: https://thegatehub.com/ ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ #ReflexiveRelation #Relations #DiscreteMathematics #Mathematics #Math #SetTheory #Sets #MathTutorial #MathVideos #MathEducation #LearningMath #MathHelp #MathConcepts #MathematicalConcepts #OperationsOnRelations #MathematicalRelations #MathematicalOperations #MathematicalProperties #MathematicalFunctions #MathematicalNotations #ReflexiveRelation #IrreflexiveRelation #PropertiesOfRelations #RelationsInMaths #ReflexiveClosure #DiscreteMathematics #DiscreteMaths #GateCSE #GATE2026 #TheGateHub #GatePreparation #BooleanMatrix #DigraphMethod #EquivalenceRelation #PartialOrder #MFCS #MathematicalFoundations #EngineeringStudents #BTechCSE #SemesterExams #GateMathematics #PlacementPreparation #LearnWithGatehub #DiscreteMathLecture16