Ex 1.4, 10 - Find which has identity (i) a*b = a - b - Binary operations: Identity element

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  1. Chapter 1 Class 12 Relation and Functions
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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

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