Set class-5

Empty Set 

The set is empty! This means that there are no elements in the set. This set is represented by ϕ (read as phi) or {}. An empty set is hence defined as:

Definition: If a set doesn’t have any elements, it is known as an empty set or null set or void set. For e.g. consider the set,

P = {x : x is a leap year between 1904 and 1908}

Between 1904 and 1908, there is no leap year. So, P = ϕ.

 Notes,p= {x:x read as x such that x}

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Singleton Set

If a set contains only one element, then it is called a singleton set. For e.g.

A = {x : x is an even prime number}

B = {y : y is a whole number which is not a natural number}

Finite Set

In this set, the number of elements is finite. All the empty sets also fall into the category of finite sets.

Definition: If a set contains no element or a definite number of elements, it is called a finite set.

If the set is non-empty, it is called a non-empty finite set. Some examples of finite sets are:
A = {x : x is a month in a year}; Set A will have 12 elements

B={y: y is the zero of a polynomial (x4 − 6x2 + x + 2)(x4 − 6x2 + x + 2)}; Set B will have 4 zeroes

Infinite Set

Just contrary to the finite set, it will have infinite elements. If a given set is not finite, then it will be an infinite set.

For e.g.

A = {x : x is a natural number}; There are infinite natural numbers. Hence, A is an infinite set.

B = {y: y is the ordinate of a point on a given line}; There are infinite points on a line. So, B is an infinite set.

Extra Tips ; Why are Sets Important?

Sets are the fundamental property of mathematics. Now as a word of warning, sets, by themselves, seem pretty pointless. But it's only when we apply sets in different situations do they become the powerful building block of mathematics that they are.

In the given figure, a set of apple, mango, papaya, banana and orange is shown. In this set, every member is called element. Can you write down how these sets are represented? There are different ways to represent the sets. The easiest way to represent a set is by writing any English capital letter. for eg: A,B,C,D…………….Z. The elements of a set is represented by small letters. We write the set by writing any capital letter first and then giving equals sign and a curly bracket

is given { } and the elements of a set is separated by giving comma(,) . From the given figure write down the elements of sets by the above mentioned process. That set is written as {1,2,3,4,5}. Let's denote the set by C and these numbers are first five natural numbers. Here t he number of elements in the set is 5 and the set is written as: C={1, 2, 3, 4, 5} or C={5, 4, 3, 2, 1} In this way, the set can be written in any order of the elements present in the set but the repeated elements is not written in a set. For eg: {S,C,H,O,O,l] is not written but it is written as {S,C,H,O,L}. So an element is written only once

Example-1

Write down seven days of a week by listing method

Ans:  D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Example-2

What is the set of E={2,4,6,8,10} 

Ans:They are the set of first five even numbers. 

Exercise

1. Write down the following sets by listing method using the symbols:

 a. Sets of 12 Nepali months

b. Sets of English vowel letters 

c. Sets of class 5 books that you should read

 d. Sets of odd numbers less than ten

 e. Sets of numbers with no remainder when divided to 24

2. Write down the following sets into sentence:

 a. C = {cow, buffalo, horse}

 b. D = {Kathmandu, Lalitpur, Bhaktapur}

 c. S = {Nepal, India, Bangladesh, Srilanka, Pakistan,  Maldieves, Bhutan}

 d. V = {a, e, i, o, u}

 e. R = {I, II, III, IV, V}

 f. E = {10, 12, 14, 16, 18, 20} 

g. {5, 10, 15, 20, 25}