Class XI Chapter 2 – Relations and Functions Maths ______________________________________________________________________________ Question 10: The Cartesian product A A has 9 elements among which are found 1,0 and (0, 1). Find the set A and the remaining elements of A A . Solution 10: We know that if n A p n A A n A n A It is given that A 9 n A n A 9 n A n A 3 1,0 The ordered pairs We know that Since 3, n A and , n B A A a, a : a A q then n AB pq and (0, 1) are two of the nine elements of A A . it is clear that The remaining elements of set A A A 1,0,1 . Therefore, . . 1,0,and 1 are elements of A. 1, 1 , 1,1 , 0, 1 , 0,0 , 1, 1 , 1,0 , are and 1,1 . Exercise 2.2 Question 1: Let A 1,2,3...14 . Define a relation R from A to A by x, y A . Write down its domain, codomain and range. Solution 1: The relation R from A to A is given as i.e., R R x, y : 3 x y, where x, y A 1,3 , 2,6 , 3,9 , 4,12 R x, y : 3x y 0 R x, y : 3x y 0, where x, y A The domain of R is the set of all first elements of the ordered pairs in the relation. Domain of R 1,2,3,4 The whole set A is he codomain of the relation R. Codomain of R A 1, 2,3....14 The range of R is the set of all second elements of the ordered pairs in the relation. Range of R 3,6,9,12 , where 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 ______________________________________________________________________________ Question 2: Define a relation R on the set N of natural numbers by xisa naturalnumber less than 4; x, y N} the domain and the range. Solution 2: R x, y : y x 5, xis a natural number less than 4, x, y N The natural numbers less than 4 are 1, 2, and 3. R 1,6 , 2,7 , 3,8 R {( x, y) : y x 5, . Depict this relationship using roster form. Write down The domain of R is the set of all first elements of the ordered pairs in the relation. Domain of R 1, 2,3 The range of R is the set of all second elements of the ordered pairs in the relation. Range of R 6,7,8 Question 3: A 1,2,3,5 and B 4,6,9 between x and y is odd; x A, y B} Solution 3: A 1, 2,3,5 and B 4,6,9 . Define a relation R from A to B by . Write R in roster form. R x, y :thedifference between x and y is odd; x A, y B R 1,4 , 1,6 , 2,9 , 3,4 , 3,6 , 5,4 , 5,6 R {( x, y) : thedifference Question 4: The given figure shows a relationship between the sets P and Q. Write this relation (i) in setbuilder form (ii) in roster form. What is its domain and range. Solution 4: According to the given figure, (i) (ii) R 5,3 , 6, 4 , 7,5 P 5,6,7 , Q 3, 4,5 R x, y : y x 2; x P or R x, y : y x 2for x 5,6,7 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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