(1) Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, which of the following are relation from A to B ?
(i) R_{1} = {(2, 1), (7, 1)}
(ii) R_{2 }= {(–1,1)}
(iii) R_{3} = {(2, –1), (7, 7), (1, 3)}
(iv) R_{4}= {(7,–1), (0,3), (3,3), (0,7)} Solution
(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 x A. Also, find the domain and range of R. Solution
(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. Solution
(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} Solution
(ii) {(x, y) | y = x + 3, x, y are natural numbers < 10} Solution
(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 xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram. Solution
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