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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ Name:
Class: Date: 1. Given that set P = {1, 2, 3, 4} and set Q = {2, 4, 6, 8} and the relation is Q is
two times P. Represent the relation using; a) An arrow diagram b) Ordered pairs c) A graph
SOLUTION:
1
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 2. The following arrow diagram shows a relation.
q
r n
p m
F G
i) Determine the domain, codomain and the range of relation. ii) State the object of q. iii) State the image of m. SOLUTION: 3. The following set of ordered pairs shows a relation.
{(1, 1), (2, 4), (3, 9), (4, 16)}
i) Determine the domain, codomain and range of this relation. ii) State the object of 9. iii) State the image of 4.
SOLUTION:
2
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 4. The following graph shows a relation.
3 2 Set A
1
12
9
6
3
0
Set B
i) Determine the domain, codomain and range of this relation. ii) State the object of 12. iii) State the images of 1.
SOLUTION:
5. State the type of relation for the following arrow diagram.
SOLUTION:
3
6
9
b
c
a
A B
3
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 6. State the type of relation for the following ordered pairs.
{(2, 3), (2, 4), (2, 5)}
SOLUTION: 7. State the type of relation for the following graph.
SOLUTION:
18
17
16
4 3 2 1
15
0
8. The relation between set X and set Y is Y is the square root of X. Draw an arrow diagram using any suitable objects and images. State the relation for the two sets.
SOLUTION:
4
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 9. State the type of relation for the following cases. Draw the arrow diagram with
any suitable objects and images. P = {Age of students} Q = {Students in a class}
i) Set P is the domain and set Q is the range. ii) Set Q is the domain and set P is the range.
SOLUTION:
5
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 1. Given that set P = {1, 2, 3, 4} and set Q = {2, 4, 6, 8} and the relation is Q is
two times P. Represent the relation using; a) An arrow diagram b) Ordered pairs c) A graph
SOLUTION: a)
2 4 6 8 4
3 2 1
P Q
b) {(1, 2), (2, 4), (3, 6), (4, 8)} c)
4 2 3 Set P
1
2
4
6
8
Set Q
0
6
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 2. The following arrow diagram shows a relation.
q
r n
p m
F G
i) Determine the domain, codomain and the range of relation. ii) State the object of q. iii) State the image of m.
SOLUTION: i) Domain = {m, n}
Codomain = {p, q, r} Range = {p, q, r}
ii) Object of q is n. iii) Image of m is p.
3. The following set of ordered pairs shows a relation.
{(1, 1), (2, 4), (3, 9), (4, 16)}
i) Determine the domain, codomain and range of this relation. ii) State the object of 9. iii) State the image of 4.
SOLUTION: i) Domain = {1, 2, 3, 4}
Codomain = {1, 4, 9, 16} Range = {1, 4, 9, 16}
ii) Object of 9 is 3. iii) Image of 4 is 16.
7
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 4. The following graph shows a relation.
3 2 Set A
1
12
9
6
3
0
Set B
i) Determine the domain, codomain and range of this relation. ii) State the object of 12. iii) State the images of 1.
SOLUTION: i) Domain = {1, 2, 3}
Codomain = {3, 6, 9, 12} Range = {3, 6, 9, 12}
ii) Object of 12 is 3. iii) Images of 1 are 3 and 6.
5. State the type of relation for the following arrow diagram.
SOLUTION: one-to-one.
3
6
9
b
c
a
A B
8
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 6. State the type of relation for the following ordered pairs.
{(2, 3), (2, 4), (2, 5)}
SOLUTION: one-to-many.
7. State the type of relation for the following graph.
SOLUTION: many-to-one.
18
17
16
4 3 2 1
15
0
8. The relation between set X and set Y is Y is the square root of X. Draw an arrow diagram using any suitable objects and images. State the relation for the two sets.
SOLUTION:
The type of relation is one-to-many.
2
2 3
3
9
4
X Y
9
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Activity Sheet Lesson 1 Introduction to Relations ________________________________________________________________ 9. State the type of relation for the following cases. Draw the arrow diagram with
any suitable objects and images. P = {Age of students} Q = {Students in a class}
i) Set P is the domain and set Q is the range. ii) Set Q is the domain and set P is the range.
SOLUTION: i) Set P is the domain and set Q is the range.
Ram Chong
Diana 15
John 14
P Q
The type of relation is one-to-many.
ii) Set Q is the domain and set P is the range.
15
Chong
Diana Ram
14 John
P Q
The type of relation is many -to-one.
10