Prove Reflexivity, Symmetry, Transitivity | Equivalence Classes Explained | VTU BCS405A

Master equivalence relations with an important VTU exam question, explained step-by-step. Perfect for BCS405A students to understand relation properties and equivalence classes clearly. ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question: ❓ Let A = {1, 2, 3, 4, 5}. Define a relation R on A × A by (x₁, y₁) R (x₂, y₂) if and only if x₁ + y₁ = x₂ + y₂. 1️⃣ Verify that R is an equivalence relation 2️⃣ Find the equivalence class of [(2, 4)] 📆 Asked in: • June / July 2024 – Question 5(c) 📘 Subject: Discrete Mathematical Structures 📚 Subject Code: BCS405A 📌 Module 3 – Relations and Functions 📝 Topic: Equivalence Relation ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: • Definition of equivalence relation • Reflexive, symmetric, transitive properties • Working with ordered pairs • Finding equivalence classes • Solving VTU exam questions efficiently ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ Continue This Topic (Composition Law Proof)    • h ∘ (g ∘ f) = (h ∘ g) ∘ f | The Proof That...   2️⃣ Related Important Question (Relation Matrix & Digraph)    • Divisibility Relations & Digraphs Problem ...   3️⃣ Full Playlist (Watch in Order)    • Relations and Functions | BCS405A Module 3...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): Relations and Functions | BCS405A Module 3    • Relations and Functions | BCS405A Module 3...   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Topics: 1️⃣ Composite Function Inverse    • Prove gof is Invertible & Find Its Inverse...   2️⃣ Inverse Function Proof    • Prove g is Inverse of f | Step-by-Step Alg...   3️⃣ Function Counting    • From A to B: Total Functions, Injective Fu...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Move to composition laws and relation structures. 📌 Don’t stop here: Practice equivalence relations with different conditions. ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ 📙 All BCS405A Playlists: ▶️ Module 1 – Fundamentals of Logic    • BCS405A Module 1 – Fundamentals of Logic |...   ▶️ Module 2 – Properties of Integers    • BCS405A Module 2( Discrete Mathematics )   ▶️ Module 3 – Relations and Functions    • Relations and Functions | BCS405A Module 3...   ▶️ Module 4 – Recurrence and Inclusion-Exclusion    • BCS405A Module 4  ( The principle of exclu...   ▶️ Module 5 – Group Theory    • BCS405A Module 5 (Group Theory)   ━━━━━━━━━━━━━━━━━━━━━ #DiscreteMathematics #BCS405A #EquivalenceRelation #Relations #VTUMaths #EngineeringMaths #VTUExam