Sets | Math | Chapter 13 | Grade 5 | With Exercises Solution

SETS - Math Chapter-13, Grade 5:

Objectives:

Students will be able to:
Define Sets.
Define sets in picture, listing and descriptive form.
Understand different types of sets.
Inter relation among sets on the basis of elements of given sets.

Outcomes:

Students will have learnt to write the sets in different ways and list out relation between given sets.

Materials:

Collection of different objects.

Things To Know:

↺ Set is a collection of well-defined objects.
↺ An objects in a set is called it's member.
↺ We denote set by capital letters e.g. N = {1,2,3}
↺ ∈ symbol stands for belongs to and ∉ symbol stands for doesn't belong to.

13.1 Set/button

#What is a set?
#A set is a collection of well-defined objects.

Set is a collection of objects but these objects should be clearly (well) defined what they are. If they are not well-defined, there will be only one set in the world because we can insert everything in the same set. So, we can say that a set is a collection of well-defined objects.

Also Check:

Let's discuss, what is well-defined means? Let say, how many birds are there in the world? Almost the answer would be many. In this scenario, can you write down the names of all birds for the set? Of course not, it would be lengthy and takes a long tine to write their names. But when you are asked to write the names of any five domestic birds, it will be easy because it is clearly defined as "five domestic birds".

Next example, when you are given to make a set of tall girls in your school, you will be confused who are tall girls. But when you are asked to make a set of tall girls having more than 5 feet in your class, then you can easily make that set. Here, the set of tall girls with height more than 5 feet is clearly defined.

Different ways of defining Sets:

1. Picture form,
2. Listing form and
3. Descriptive form.

1. Picture form: In this form, the elements of sets are presented in the form of pictures.

A set of fruits.

A set of geometrical shapes.

2. Listing Form: Here, the elements of the set are listed as their names.

A set of fruits,
F = {apple, banana, orange, grapes}

A set of geometrical shapes,
G = {rectangle, triangle, circle, square}

3. Descriptive form: Here, the set is described according to their common properties.

A set of fruits
F = {set of four fruits that is mostly used in your home}
G = {set of four basic plane figures}

To write the name of a set, we write a capital letter and equal to sign "=" and then the names of elements inside curly bracket {} and each elements are separated by comma (,).

13.2 Types of Set/button

There are four different types of sets which are described briefly as follows:

i. Empty or Null Set.
#What is empty or null set?
↺ A set which has no elements is called empty or null set. It is determined by curly brackets { } with nothing inside. ∴ N = { }.

ii. Unit Set.
#What is Unit Set?
↺ A set which has single member is called a Unit Set. A set of tallest mountain in the world. ∴ M = { Mt. Everest }

iii. Finite Set.
#What is Finite Set?
↺ A set that contains countable number of elements is called a finite set. A set of first 5 natural numbers. ∴ N = { 1,2,3,4,5 }

iv. Infinite Set.
#What is an Infinite Set?
↺ A set that contains countless number of elements is called an infinite set. A set of natural numbers N = { 1,2,3,4, ............. }

13.3 Relations/button

One set may relate to other sets in different ways according to their type and number of elements.

i. Equal Sets:
Equal sets have same members and equal numbers of elements but in different order. Like,
A = { 1, 2, 3, 4, 5 } and B = { 5, 4, 3, 2, 1 }
Here, sets A and B have same members and equal number of elements. So, A and B are equal sets. It is denoted by A=B.
#What is equal sets?
#Sets having same members and equal numbers of elements but in different order is called equal sets.

ii. Equivalent Sets:
Equivalent sets have equal number of elements. Like,
A = { 1, 2, 3, 4, 5 } and B = { a, e, i, o u }
Here, members of sets A and B are equal. A and B are equivalent set. It is denoted by A∼B.
#What is equivalent sets?
#Sets having equal number of elements is called equivalent sets.

iii. Overlapping Sets:
Overlapping sets have some common elements. Like,
A = { 1, 2, 3, 4, 5 } and B = 2, 4, 6, 8, 10 }
Here in sets A and B, 2 and 4 are common elements. So, they are overlapping sets.
#What is overlapping sets?
#Sets having some common elements is called overlapping sets.

iv. Disjoint Sets:
Disjoint sets have no common element. Like,
A = { 1, 2, 3, 4, 5 } and B = { 6, 12, 18, 24 }
Here in sets A and B, there is no common element. So, they are disjoint sets.
#What is disjoint sets?
#Sets that do not have common elements is called disjoint sets.

Grade 5: Math Subject-Chapter:13 - SETS: Exercise 13.1 (With Solution)/button

1. Express the following sets in listing form.

a. The set of seven days in a week.
Solution: D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

b. The set of four pet animals.
Solution: P = {Dog, Cat, Rabbit, Horse}

c. The set of vowel letter of English alphabet.
Solution: V = {a, e, i, o, u}

d. The sets of months of a year that starts with 'J'.
Solution: J = {January, June, July}

e. The set of even number less than 10.
Solution: E = {2, 4, 6, 8}

f. The set of first five multiples of 3.
Solution: M = {3, 6, 9, 12, 15}

g. The set of digits in 325346.
Solution: D = {3, 2, 5, 4, 6}

2. Write the following set in descriptive form.

a. S = {Nepal, India, Pakistan, Bhutan, Maldives, Sri-lanka, Afghanistan, Bangaladesh}
Solution:
The given set 'S = {Nepal, India, Pakistan, Bhutan, Maldives, Sri-lanka, Afghanistan, Bangaladesh}' contains the countries of South Asia. So, we can represent the above set in descriptive form as follows.
S is the set of all eight South Asian countries.
Or,
S = {set of eight South Asian countries}

b. M = {5, 10, 15, 20, 25}
Solution:
The given set 'M = {set of first five multiples of 5}' contains the first five multiples of 5. So, we can represent the above set in descriptive form as follows.
M is the set of the first five multiples of 5.
Or,
M = {set of first five multiples of 5}

c. V = {a, e, i, o, u}
Solution:
The given set 'V = {a, e, i, o, u}' is set of vowel letters of English alphabet. So, we can represent the above set in descriptive form as follows.
V is the set of Vowel letters of English alphabet.
Or,
V = {set of vowel letters of English alphabet}

d. F = {Rose, Marigold, Lotus, Lily}
Solution:
The given set 'F = {Rose, Marigold, Lotus, Lily}' is set of four flowers that are very beautiful. So, we can represent the above set in descriptive form as follows.
F is the set of four flowers that are very beautiful.
Or,
F = {set of four flower that are very beautiful}

e. D = {Kathmandu, Lalitpur, Bhaktapur}
Solution:
The given set 'D = {Kathmandu, Lalitpur, Bhaktapur}' is the set of three districts of Bagmati province. So, we can represent the above set in descriptive form as follows.
D is the set of three districts of Bagmati province.
Or,
D = {set of three districts of Bagmati province}

f. N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Solution:
The given set 'N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}' is the set of natural number upto 10. So, we can represent the above set in descriptive form as follows.
N is the set of natural number upto 10.
Or,
N = {sets of natural numbers upto 10}

Grade 5: Math Subject-Chapter:13 - SETS: Exercise 13.2 (With Solution)/button

1. Write the type of the following sets.

a. The set of whole numbers less than 15.
Solution: 'The set of whole numbers less than 15' is a Finite Set.

b. The set of factors of 24.
Solution: 'The set of factors of 24' is a Finite Set.

c. The set of first five multiples of 7.
Solution: 'The set of first five multiples of 7' is a Finite Set.

d. Set N = { 1, 2, 3, 4, 5, ....}
Solution: 'Set N = { 1, 2, 3, 4, 5, ....}' is an Infinite Set.

e. The set of mountains all over the world.
Solution: 'The set of mountains all over the world' is an Infinite Set.

f. The set of even number in between 5 and 7.
Solution: Here, even number between 5 and 7 is 6. So, it has a single member/element. Therefore, 'The set of even number in between 5 and 7' is Unit Set.

g. The set of days in a week that starts with U letter.
Solution: Here, the days in a week that starts with U letter is zero. So, 'The set of days in a week that starts with U letter' is an Empty or Null Set.

2. List out the relations between the given sets.

a. A = { a, b, c, d, e } and B = { m, n, o, p, q }
Solution: 'A = { a, b, c, d, e } and B = { m, n, o, p, q }' is an Equivalent Sets. ∵ They have equal number of elements.

b. O = { 1, 3, 5, 7 } and E = { 2, 4, 6, 8, 10 }
Solution: 'O = { 1, 3, 5, 7 } and E = { 2, 4, 6, 8, 10 }' is a Disjoint Sets. ∵ They have no common elements.

c. M = { a, e, i, o , u } and C = { e, f, g, h, i }
Solution: 'M = { a, e, i, o , u } and C = { e, f, g, h, i }' is a Overlapping Sets. ∵ They have some common elements.

d. A = { 10, 11, 12, 13, 14, 15 } and B = { 5, 10, 15, 20 }
Solution: 'A = { 10, 11, 12, 13, 14, 15 } and B = { 5, 10, 15, 20 }' is a Overlapping Sets. ∵ They have some common elements.

e. M is the set of the tallest mountain in the world.
Solution: 'M is the set of the tallest mountain in the world' is an Infinite Sets. ∵ It has countless number of elements (tallest mountains).

f. E is the set of even numbers in between 6 and 8.
Solution: 'E is the set of even numbers in between 6 and 8' is an Empty or Null Sets. ∵ It has no elements (even number between 6 and 8).

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