Exercise 1.2: Relations

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 = 2y, 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 A1, A2, A3, A4  and A5  were Assistants; C1, C2, C3, C4 were Clerks; M1, M2, M3 were managers and E1, E2 were Executive officers and if the relation R is defined by xRy, 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}