Maths Book back answers and solution for Exercise questions - Mathematics : Relation: Problem Questions with Answer

Exercise 1.2

1. Let *A* = {1,2,3,7} and *B* = {3,0,–1,7}, which of the following are relation from *A* to *B* ?

(i) R1 = {(2,1), (7,1)}

(ii) R2= {(–1,1)}

(iii) R3 = {(2,–1), (7,7), (1,3)}

(iv) R4= {(7,–1), (0,3), (3,3), (0,7)}

2. Let *A*={1,2,3,4,...,45} and *R* be the relation defined as “is square of” on *A*. Write R as a subset of *A* ×*A* . Also, find the domain and range of R.

3. A Relation R is given by the set {(*x* , *y*) / *y* = *x* + 3, *x* ∈ {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

4. Represent each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set in roster form, wherever possible.

(i) {(*x*,*y*)|*x* = 2*y*, *x* ∈{2,3,4,5}, *y* ∈{1,2,3,4}

(ii) {(*x*,*y*)|*y* = *x*+3, *x*, *y* are natural numbers < 10}

5. A company has four categories of employees given by Assistants (*A*), Clerks (*C*), Managers (*M*) and an Executive Officer (*E*). The company provide ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories *A*, *C*, *M *and *E *respectively. If *A*1, *A*2, *A*3, *A*4 and *A*5 were Assistants; *C*1, *C*2, *C*3, *C*4 were Clerks; *M*1, *M*2, *M*3 were managers and *E*1, *E*2 were Executive officers and if the relation R is defined by *x*R*y*, where *x *is the salary given to person *y*, express the relation R through an ordered pair and an arrow diagram.

Answers:

1.(i) Not a relation (ii) Not a relation (iii) Relation (iv) Not a relation

2. {1, 2, 3, 4, 5, 6} , {1, 4, 9, 16, 25, 36} 3. {0,1,2,3,4,5}, {3, 4, 5, 6, 7, 8}

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