Exercise 1.2: Relations - Problem Questions with Answer, Solution
Question 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) \(R_4 = \{(7,–1), (0,3), (3,3), (0,7)\}\)
Question 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 \(A \times A\). Also, find the domain and range of R.
Question 3
A Relation R is given by the set \(\{(x, y) | y = x + 3, x \in \{0, 1, 2, 3, 4, 5\}\}\). Determine its domain and range.
Question 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) \(\{(x,y) | x = 2y, x \in \{2,3,4,5\}, y \in \{1,2,3,4\}\}\)
(ii) \(\{(x,y) | y = x+3, x, y\) are natural numbers \(< 10\}\)
Question 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.
Quick Answers
1. (i) Not a relation (ii) Not a relation (iii) Relation (iv) Not a relation
2. Domain: \(\{1, 2, 3, 4, 5, 6\}\), Range: \(\{1, 4, 9, 16, 25, 36\}\)
3. Domain: \(\{0,1,2,3,4,5\}\), Range: \(\{3, 4, 5, 6, 7, 8\}\)
