Set-builder form of writing sets: Instead of listing the elements, If a set is defined in words with the common property of its elements, it is said to be written in the set builder form for...
E.g.:: B = {x/ x is a natural number less than 10}
C = {x/ x is a day in the week}
D = {x/ x is a colour in the rainbow}
All the above sets starts with a symbol x followed by a vertical line then the common property of its elements. These sets are written in set builder form Types of sets.
Consider the following sets:
1) X = {x/ x is a vowel in the word sky}
2) Y = {x/ x is a primary colour that begins with I}
3) Z = {x/ x + 3 = 5 and x is a natural number greater then 2}
The letters of the word sky are s, k and y
All these are consonants and not vowels
The set X does not contain any elements.
In the Second example, the primary colours are Red, Blue and Green. All these colours do not start with the letter 'I'. Therefore the set Y does not contain any element. It is empty.
In the Third example, two conditions are to be satisfied i.e., X + 3 = 5 and X is a natural number greater than 2.
X + 3 = 5
X = 2 but as the second condition says that the number must be greater than 2 we are left with no number that satisfies both the condition.Set Z is also an empty set.
10th Maths New Syllabus SETS - Roster Form of Writing Sets
Examples of sets.
1) The Collection of English alphabets.
a, b, c, d, ... x, y, z
2) The collection of Natural numbers
1, 2, 3, ...........
3) The Collection of Prime numbers
2, 3, 5, 7,..............
4) The Collection of the devices of a computer the input device. The central
processing unit, the output device
Examples of collections that are not sets
1) The collection of 5 Tasty sweet dishes.
2) The collection of interesting novels.
3) The collection of easy problems in X Maths text book.
4) The collection of beautiful dresses.
A Set is denoted by upper case letters A, B, C, D,.......... etc.
We have seen the different sets of Numbers in the chapter Real Numbers.
Roster form of writing a set:
When all the elements in the set are listed down separated by commas within
curly brackets, the set is said be written in Roster form.
All the above sets are written in Roster form.
Consider the set B of all multiples of 2 less than 20
B = {2, 4, 6, 8,. .........18}
We can write the multiples of 2 in the following manner
B = {18, 16, 14, 12 ,..........2} or
B = {2, 12, 4, 14, 6, 16, 8, 18, 10}
that is the order is which the elements in the set are listed is immaterial.
Consider the following example:
The set M of all the letter in the world 'mathematics'
M = {m, a, t, h, e, i c, s}
While writing the set in the Roster form, the elements are not repeated i.e, the
letters that are repeated in the word mathematics (m, a, t) are not written twice in the set.
From the above two examples we can say that when a set is written in the Roster form
(i) The order of listing the elements is immaterial
(ii) The elements in the set are not repeated.
1) The Collection of English alphabets.
a, b, c, d, ... x, y, z
2) The collection of Natural numbers
1, 2, 3, ...........
3) The Collection of Prime numbers
2, 3, 5, 7,..............
4) The Collection of the devices of a computer the input device. The central
processing unit, the output device
Examples of collections that are not sets
1) The collection of 5 Tasty sweet dishes.
2) The collection of interesting novels.
3) The collection of easy problems in X Maths text book.
4) The collection of beautiful dresses.
A Set is denoted by upper case letters A, B, C, D,.......... etc.
We have seen the different sets of Numbers in the chapter Real Numbers.
Roster form of writing a set:
When all the elements in the set are listed down separated by commas within
curly brackets, the set is said be written in Roster form.
All the above sets are written in Roster form.
Consider the set B of all multiples of 2 less than 20
B = {2, 4, 6, 8,. .........18}
We can write the multiples of 2 in the following manner
B = {18, 16, 14, 12 ,..........2} or
B = {2, 12, 4, 14, 6, 16, 8, 18, 10}
that is the order is which the elements in the set are listed is immaterial.
Consider the following example:
The set M of all the letter in the world 'mathematics'
M = {m, a, t, h, e, i c, s}
While writing the set in the Roster form, the elements are not repeated i.e, the
letters that are repeated in the word mathematics (m, a, t) are not written twice in the set.
From the above two examples we can say that when a set is written in the Roster form
(i) The order of listing the elements is immaterial
(ii) The elements in the set are not repeated.
10th Maths New Syllabus Bit Bank - Sets Chapter for AP and Telangana
Consider the following examples of Different items.
1. Bat, ball, gloves, wickets, pads
2. Bag, Text Books, Note Books, Pen, Pencil, Eraser, Sharpener, Lunch Box, Water Bottle
3. a, e, i. o, u
All these examples are the collections of items/ objects. Each Example has
something is common. In First Example we see things of a cricket kit, In Second
Example things that are carried to school. Third example vowels. These are well
defined collection of objects or ideas.
A well - defined collection of objects or ideas is known as a set.
The meaning of the phrase "Well - defined" is
(i) All the objects in the set should have a common feature or property.
(ii) It should be possible to decide whether any given object belongs to the set or
not consider the example.
"The collection of 5 good books in the school library".
As the words "good books" are subjective in nature each student have their own
collection of 5 books. A students who is interested in comics picks, comics books.
A student who is interested in maths may pick 5 Maths related books. Similarly a
Science student picks 5 Science related books.
Therefore there is no uniformity in the collection by different students. Hence
"the collection of 5 good books in the school library" is not a well defined set.
In the above example, it is not possible to decide whether a given book belongs
or does not belong to the collection of objects.
If the same example is considered as "The collection of new text books of X
Class" The Collection is considered as a set.
1. Bat, ball, gloves, wickets, pads
2. Bag, Text Books, Note Books, Pen, Pencil, Eraser, Sharpener, Lunch Box, Water Bottle
3. a, e, i. o, u
All these examples are the collections of items/ objects. Each Example has
something is common. In First Example we see things of a cricket kit, In Second
Example things that are carried to school. Third example vowels. These are well
defined collection of objects or ideas.
A well - defined collection of objects or ideas is known as a set.
The meaning of the phrase "Well - defined" is
(i) All the objects in the set should have a common feature or property.
(ii) It should be possible to decide whether any given object belongs to the set or
not consider the example.
"The collection of 5 good books in the school library".
As the words "good books" are subjective in nature each student have their own
collection of 5 books. A students who is interested in comics picks, comics books.
A student who is interested in maths may pick 5 Maths related books. Similarly a
Science student picks 5 Science related books.
Therefore there is no uniformity in the collection by different students. Hence
"the collection of 5 good books in the school library" is not a well defined set.
In the above example, it is not possible to decide whether a given book belongs
or does not belong to the collection of objects.
If the same example is considered as "The collection of new text books of X
Class" The Collection is considered as a set.
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