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Chapter 1 Class 12 Relation and Functions
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Ex 1.4, 10 - Find which has identity (i) a*b = a - b - Binary operations: Identity element

Ex 1.4, 10 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.4, 10 - Chapter 1 Class 12 Relation and Functions - Part 3
Ex 1.4, 10 - Chapter 1 Class 12 Relation and Functions - Part 4
Ex 1.4, 10 - Chapter 1 Class 12 Relation and Functions - Part 5
Ex 1.4, 10 - Chapter 1 Class 12 Relation and Functions - Part 6

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Ex 1.4, 10 Find which of the operations given above has identity. a * b = a b e is the identity of * if a * e = e * a = a i.e. a e = e a = a There is no possible value of e where a e = e a So, * has no identity element in Q Ex 1.4, 10 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (ii) a * b = a2 + b2 e is the identity of * if a * e = e * a = a i.e. a2 + e2 = e2 + a2 = a There is no possible value of e where a2 + e2 = e2 + a2 = a So, * has no identity element in Q Ex 1.4, 10 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (iii) a * b = a + ab e is the identity of * if a * e = e * a = a i.e. a + ae = e + ae = a There is no possible value of e where a + ae = e + ae = a So, * has no identity element in Q Ex 1.4, 10 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (iv) a * b = (a b)2 e is the identity of * if a * e = e * a = a i.e. (a e)2 = (e a)2 = a There is no possible value of e where (a e)2 = a So, * has no identity element in Q Ex 1.4, 10 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (v) a * b = ab/4 e is the identity of * if a * e = e * a = a i.e. ae/4 = ea/4 = a Which is possible if e = 4 So, 4 is the identity element of * Ex 1.4, 10 Let * be a binary operation on the set Q of rational numbers as follows. Find which are associative and which are commutative : (vi) a * b = ab2 e is the identity of * if a * e = e * a = a i.e. ae2 = ea2 = a There is no possible value of e where ae2 = ea2 = a So, * has no identity element in Q

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.