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BOARDS PREPARATIONS MADE EASY RELATIONS AND BINARY OPERATIONS CBSE AND STATE BOARDS CLASS 12 PREPARED BY: ER. VINEET LOOMBA IITIAN IIT-IEE MENTOr

100% SUCCESS IN CLASS 12 BOARD EXAMS ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. Youtube, Founder @ vi neetloomba.com unacademy & Many of my students have scored 100/100 & Currently running my own Coaching Institute for JEE Main and Advanced Search vineet loomba unacadem "on G00GLE

BOARDS PREPARATIONS MADE EASY RELATIONS AND BINARY OPERATIONS CBSE AND STATE BOARDS CLASS 12 PREPARED BY: ER. VINEET LOOMBA IITIAN IIT-IEE MENTOr

100% SUCCESS IN CLASS 12 BOARD EXAMS EXMPLELet A- {1,2,3,4). Let R be the equivalence relation on Ax A defined by Let A= {1, 2, 3,4. Let R be the equivalence relation on A A defined by ( a,b)R(c,d)iff a+d-b+c. Find the equivalence class (1,3 )] SUCCESS IN MATHEMATICS CLASS 12 BOARDS ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN CLASS 12 BOARD EXAMS EXAMPLE: Show that the relation R in the set Nx N defined by (a, b)R(c, d) iff a2-d2-b4c"Ya,b,c,de N, is an equivalence relation. Let (a.b)eNxN. Then a2 +b2-b2 +a2..(a,b)R(a, b) Hence, R is reflexive Let (a, b), (c,d),(e, f)e N N be such that (a,b)R(c,d),(c, d)R(et) Let (a, b), (c,d) ENx N be such that (a, b)R(c,d) => a2 + d2-b2 + c2 2+b2-d2+a2 (c,d)R(a, b) (a, b)R(e,f) Hence, R is symmetric Hence, R is transitive. SUCCESS IN MATHEMATICS CLASS 12 BOARDS ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN CLASS 12 BOARD EXAMS EXAMPLE: Give an example to show that the relation R in the set of natural numbers, defined by R-(x, y), x, y EN, x<y is not transitive. (8, 3)ER, (3, 2)e R but (8, 2) R SUCCESS IN MATHEMATICS CLASS 12 BOARDS ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN CLASS 12 BOARD EXAMS EXAMPLE: Let N be the set of all natural numbers and R be the relation in NxN defined by (a,b) R (c,d) if ad-bc. Show that R is an equivalence relation. For any (a, b)e NxN, ab ba Let (a, b) R(c, d) and (c, d) R(e, f for a, b, c, d, e, f eN then ad - bc and cf de (a, b) R (a, b). Thus R is reflexive. Let (a, b) R(c, d) for any a, b, c, dEN. R is transitive .. ad-bc adcf bcde or af be(a, b) R(e, f) cb-da(c, d) R(a, b) . R is symmetric SUCCESS IN MATHEMATICS CLASS 12 BOARDS ER. VINEET LOOMBA (IIT ROORKEE)

100% SUCCESS IN CLASS 12 BOARD EXAMS Save Save for this Course (Free) MOST IMPORTANT QUESTIONS IN MATHEMATICS Recommend Lessons (Like) TEE MAIN AND ADVANCED PREPARED ER. VINEET LOOMS . Rate and Review the Course MADE EASY 1ITIAN I IT-IEE MENTOR 00:00 05:46 SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED CIIT-IEE) Comments ib 91 likes 18 comments Share HINDI Crash Course Maths Sharing with friends (Hindi) Most Important Questions in IIT-JEE Mathematics (Chapter- Wise) Vineet Loomba 11k Followers Follow 5.0 (51 ratings) Edit review SUCCESS IN MATHEMATICS CLASS 12 BOARDS ER. VINEET LOOMBA (IIT ROORKEE)