Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ 1,2,3,4 and B 1,5,9,**11**,15,16 A A B { 1,1 , 1,5 , 1,9 , 1,**11** , 1,15 , 1,16 , 2,1 , 2,5 , 2,9 , 2,**11** , 2,15 , 2,16 3,1 , 3,5 , 3,9 , 3,**11** , 3,15 , 3,16 , 4,1 , 4,5 , 4,9 , 4,**11** , 4,15 , 4,16 } It is given that f 1,5 , 2,9 , 3,1 , 4,5 , 2,**11** (i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product . Thus, f is a relation from A to B. (ii) Since the same first element i.e, 2 corresponds to two different images i.e., 9 and **11**, relation f is not a function. AB Question **11**: Let f be the subset of Justify your answer. Solution **11**: ZZ The relation f is defined as defined by f ab, a b : a, b Z f ab, a b : a, b Z . If f a function from Z to Z: We know that a relation f from a set A to a set B is said to be a function if every element of set A has unique images in set B. Since 2,6, 2, 6 Z, 26, 2 6 , 2 6, 2 6 f 12,8 , 12, 8 f i.e., It can be seen that the same first element i.e., 12 corresponds to two different images i.e., 8 and 8. Thus, relation f is not a function. Question 12: Let A 9,10,**11**,12,13 Find the range of f. Solution 12: A 9,10,**11**,12,13 Prime factor of 9 = 3 Prime factors of 10 = 2, 5 Prime factor of **11** = **11** Prime factor of 12 = 2, 3 Prime factor of 13 = 13 and let f : A N be defined by f n the highest prime factor of n. and let f : A N is defined as f n The highest prime factor of n Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ 9 f The highest prime factor of 9 = 3 f 10 The highest prime factor of 10 = 5 f **11** The highest prime factor of **11** = **11** f 12 The highest prime factor 12 = 3 f 13 The highest prime factor of 13 = 13 The range of f is the set of all Range of f 3,5,**11**,13 f n , where n A . Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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