10th Maths Guide English Medium
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10th maths Guide English Medium
10th maths Exercise 1.2 Solution (Answers)
10th maths Example1.2 Solution // Relation and functions
10th maths "Example 1.4" solution
Question : Let A = {3, 4, 7, 8} and B = {1, 7, 10}. Which of the following sets are relations from A to B ?
(i) R1 = {(3, 7), (4, 7), (7, 10), (8, 1)}
(ii) R2 = {(3, 1), (4, 12)}
(iii) R3 = {(3, 7), (4, 10), (7, 7), (7, 8), (8, 11), (8, 7), (8, 10)}
Solution :
A×B = {(3, 1), (3, 7), (3, 10), (4, 1), (4, 7),
(4,10), (7,1), (7,7), (7,10), (8, 1), (8, 7), (8, 10)}
(i) We note that R1 ⊆ A × B. Thus, R1 is a relation from A to B.
(ii) Here, (4, 12) ∈ R2, but (4, 12) ∉ A × B. So, R2 is not a relation from A to B.
(iii) Here, (7, 8) ∈ R3, but (7, 8) ∉ A × B. So R3 is not a relation from A to B.
10th maths "Example 1.5"solution /Relation and function
Question : The arrow diagram shows a relationship be-tween the sets P and Q. Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R.
Solution :
(i) Set builder form of R = {(x, y) | y = x – 2, x ∈ P, y ∈ Q}
(ii) Roster form R = {(5, 3), (6, 4), (7, 5)}
(iii) Domain of R = {5, 6, 7} and range of R = {3, 4, 5}
10th maths EXERCIsE 1.2 solution question number 1 / relation and functions
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 :
Given A = {1, 2, 3, 7}, B = {3, 0, –1, 7}
∴ A × B = {(1, 3), (1, 0), (1, –1), (1, 7),
(2, 3), (2, 0), (2, –1), (2, 7),
(3, 3), (3, 0), (3, –1), (3, 7),
(7, 3), (7, 0), (7, –1), (7, 7)}
i) R1 = {(2, 1), (7, 1)}
(2, 1) ∈ R1 but (2, 1) ∉ A × B
∴ R1 is not a relation from A to B.
ii) R2 = {(–1, 1)}
(–1, 1) ∈ R2 but (–1, 1) ∉ A × B
∴ R2 is not a relation from A to B.
iii) R3 = {(2, –1), (7, 7), (1, 3)}
We note that R3 ⊆ A × B
∴ R3 is a relation.
iv) R4 = {(7, –1), (0, 3), (3, 3), (0, 7)} (0, 3), (0, 7) ∈ R4 but not in A × B.
∴ R4 is not a relation.
10th maths EXERCIsE 1.2 solution question number 2 / relation and functions
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.
Solution :
Given A = {1, 2, 3, 4, ........ 45}
R : “is square of”
R = {1, 4, 9, 16, 25, 36}
Clearly R is a subset of A.
∴ Domain = {1, 2, 3, 4, 5, 6}
∴ Range = {1, 4, 9, 16, 25, 36}
10th maths EXERCIsE 1.2 solution question number 3 / relation and functions
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 :
Given R = {(x, y) / y = x + 3,
x ∈ {0, 1, 2, 3, 4, 5}}
x = 0 ⇒ y = 3 x = 1 ⇒ y = 4
x = 2 ⇒ y = 5 x = 3 ⇒ y = 6
x = 4 ⇒ y = 7 x = 5 ⇒ y = 8
∴ R = {(0, 3), (1, 4), (2, 5), (3, 6), (4, 7), (5, 8)}
∴ Domain : {0, 1, 2, 3,4, 5}
Range : {3, 4, 5, 6, 7, 8}
10th maths EXERCIsE 1.2 solution question number 4 / relation and functions
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}
Solution : i) {(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y∈{1, 2, 3, 4} a)
Arrow diagram :
b) Graph :
c) a set in roster : z {(2, 1), (4, 2)}
ii) {(x, y) | y = x + 3, x, y are natural numbers < 10}
a) Arrow Diagram :
b) Graph :
c) a set in roster :
= {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)}
10th maths EXERCIsE 1.2 solution question number 1 / relation and functions
5. A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Off icer (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.
Solution :
a) Ordered Pair :
{(10000, A₁), (10000, A₂), (10000, A₃), (10000, A₄), (10000, A₅), (25000, C₁),
(25000, C₂), (25000, C₃), (25000, C₄),
(50000, M₁), (50000, M₂), (50000, M₃),
(100000, E₁), (100000, E₂s).
b) Arrow Diagram :
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