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Annotated Notes of this session: https://shorturl.at/mS289 (Please Like & Comment. Thank You.) Complete Analysis of GATE CSE 2021 question on Circular Relations. A relation R is said to be circular if aRb and bRc together imply cRa. Theorem: A binary relation R over a set A is an equivalence relation if and only if it is reflexive and cyclic. Lemma 1: If R is an equivalence relation over a set A, then R is reflexive and cyclic. Lemma 2: If R is a binary relation over a set A that is reflexive and cyclic, then R is an equivalence relation. GATE | GATE CS 2021 | Set 1 | Question 53 A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct? (A) If a relation S is reflexive and symmetric, then S is an equivalence relation. (B) If a relation S is circular and symmetric, then S is an equivalence relation. (C) If a relation S is reflexive and circular, then S is an equivalence relation. (D) If a relation S is transitive and circular, then S is an equivalence relation. Crack GATE Computer Science Exam with the Best Course. ➤ Join "GO Classes #GateCSE Complete Course": https://www.goclasses.in/courses/GATE... ➤ Join "GATE CSE+DA Combined Course": https://www.goclasses.in/courses/GATE... ➤ Join "GO Classes #GateDA Complete Course": https://www.goclasses.in/courses/GATE... ➤ Download GO Classes Android APP: https://play.google.com/store/apps/de... ➤ GO Classes GATE DA YouTube Channel: / @goclassesforgateda ---------------------------------------------------- #GoClasses Website : https://www.goclasses.in/ #GOClasses ALL Links : https://linktr.ee/goclasses ➤ Join GATEOverflow + GoClasses Combined GATE CSE TEST SERIES for Best Quality questions for GATE CSE Preparation, Here: https://gateoverflow.in/blog/14987/ga... ---------------------------------------------------- ➤Join GATE Overflow & GO Classes Telegram Groups for GATE CSE Doubt Discussions: 1. https://t.me/GoClasses_CSE 2. https://t.me/GATECSE_Goclasses 3. https://t.me/gateoverflow_cse ---------------------------------------------------- ➤ Watch Complete Discrete Mathematics and Complete Engineering Mathematics Courses on GO Classes( FREE for ALL learners) : https://www.goclasses.in/s/store/ Complete #Discrete_Mathematics Course(FREE) Link : https://www.goclasses.in/courses/Disc... Complete #Engineering_Mathematics Course(FREE) Link : https://www.goclasses.in/courses/Engi... Download GATEOverflow GATE Previous Years Questions(GATE CSE PYQs) Books here: https://github.com/GATEOverflow/GO-PD... ---------------------------------------------------- Feel free to Contact Us for any query. ➤ GO Classes Contact : (+91)63025 36274 (+91)9468930964 GO Classes Mail ID : contact@goclasses.in #gate2025 #goclasses #computerscience #gateda #gatecs #computer_science #gatecse