Sets in mathematics are just a collection of things, numbers, days of the week, sports items, articles of stationery, electric goods, etc. We mostly called these things a group of items. In short, these groups of items are called sets in mathematics. Everything in a group of items is called elements of sets in mathematics. Now, we are going to study the following concepts of sets in mathematics that are:
- What is the History of Sets in Math?
- What are Daily Life Examples
- What is the Definition of the set?
- What is meant by well-defined objects in sets?
- What is meant by Distinct in sets?
- Practice Questions and Examples For Sets
What is the History of Sets in Math?
A great Mathematician of the 19th century named George Cantor. He gave us the proper idea of a set that we are using now in different branches of sets. The concept of sets is originally taken from the Set Theory.
Set Theory is a branch of mathematical logic that deals with the collection of objects which are called sets in mathematics.
What is Daily Life Examples?
Now, you are going to learn about sets in daily life.
In daily life, you often listen to some words which represent the collection of things like:
Pile of papers
Team of players
Group of friends
Bundle of sticks
And so on.
But in mathematics, we use only a single word in place of all such types of words known as “set”. Here set shows the collection of things like:
Set of numbers
Set of geometrical shapes
- Set of Articles of stationary
What is the Definition of the set?
Now, we can define the set as:
"The collection of objects/ things that are well-defined as well as distinct is called a set in mathematics".
In a set, the objects/ things are called members/elements of a set. So, A set is made up of elements/ members. These elements may be numbers, alphabetical letters, variables, geometrical shapes, etc. But there are some rules for these elements that are given below
What is meant by well-defined Objects in Sets?
A particular property of anything that allows it to be an element of a set or not is called its well-defined property.
Let us understand it by the following examples of collections:
The collection of favorite players in a team
The collection of sour grapes
The collection of most beautiful friends in a class
Here, notice that the words good, sour, and most beautiful are not well-defined because team players may be favorite for one person, but may not be for another. So, the above sets are not well-defined.
Well-defined examples of sets are
The set of natural numbers
The set of vowels in English alphabets
What do you mean by the word “Distinct” in sets?
Distinct means that the same objects/things do not appear more than once in a set.
For Example,
The set of letters of the word ‘Pakistan’ is
｛P, a, k, i , s, t, n｝
Here. the letter ‘a’ has been written only once. If you write ‘a’ twice then the above set is not a set.
Sets Math Examples with Answers
Example 1: Identify whether the following are sets or not
A = {a, b, c, d},
B = {a, b, b, c},
C = {q, u, e, e, n},
E = The set of naughty boys
and F = The set of Pakistani actors
Solution:
A = {a, b, c, d},
This is a set because the elements are distinct and well-defined.
B = {a, b, b, c},
This is not set because the elements are not distinct.
C = {q, u, e, e, n},
This is not a set because the elements are not distinct and well-defined.
E = The set of naughty boys
This is not a set because the elements are not well-defined.
F = The set of Pakistani actors
This is not a set because the elements are not distinct and well-defined.
Sets Math Practice Questions with Answers
Identify the following collections are sets or not and also give the reason?(i) The set of domestic animals.
(ii) The set of natural numbers less than 7.
(iii) The brave boys of the class.
(iv)The set of pets.
(v) The five cities of Pakistan.
(vi) The players of the Pakistan hockey team.
(vii) The easy questions of a test.
(viii) The set of library books.
(ix) The set of beautiful girls.
(x) The set of poor people.
(xi) The set of students in the 6th class.
(xii) The set of fish in the sea.
(xiii) The set of intelligent boys in a school.
(xiv) The set of chairs in a classroom.
(xv) {p, i, z, z, a}
(xvi) {2, 3, 5, 7}
(xvii) {1, 2, 2, 4}
(xviii){p, a, r, r, o, t}
(xix) {f, a, i, s, a, l}
(xx) {9,3,5,1}