# Ex 1.4, 10 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 17, 2018 by Teachoo

Last updated at Dec. 17, 2018 by Teachoo

Transcript

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

Chapter 1 Class 12 Relation and Functions

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.