RELATION IN SET THEORY WORKSHEET

(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)}          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 A₁, A₂, A₃, A₄and 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.     Solution

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