Subset: If A and B are two given sets and every element of set B is also an element of set A, then B is a subset of A which is symbolically written as B ⊆ A. It is read as ‘B is a subset of A’ or ‘B subset A‘.
e.g. If A \(=\) {11, 12, 13, 14, 15, 16, 17, 18} and B \(=\) {11, 13, 17} then, every element of set B is also an element of set A. Thus, B ⊆ A
Natural Numbers
Whole Numbers
Integers
Natural Numbers
Whole Numbers
Integers
12, 32, 9
12, 0, 32, 9
12, − 7, 0, 32, − 1, 9
Classify the following numbers as Even Numbers, Odd Numbers and Prime Numbers: 11, 14, 27, 31, 52, 97, 2
Even Numbers
Odd Numbers
Prime Numbers
Even Numbers
Odd Numbers
Prime Numbers
14, 52, 2
11, 27, 31, 97
12, − 7, 0, 32, − 1, 9
Important Points
Sets:
A well defined collection of objects is called a set.
Sets are denoted by capital alphabets like A, B, P, Q etc. e.g.
N = The set of Natural Numbers
W = The set of Whole Numbers
P = The set of colours in a rainbow
The elements of a set are generally denoted by small alphabets.
Writing a set:
While writing a set,
All the elements are listed in curly brackets.
The elements are separated by commas.
The order in which the elements are written is not important.
Each element is written only once.
e.g.
The set of even numbers between 1 and 10 can be written in the list form as follows: A = {2, 4, 6, 8, 10} OR A = {4, 8, 10, 2, 6}
The set of letters in the word ‘mathematics’ is written as follows: {m, a, t, h, e, i, c, s}
Number of elements in a set:
Suppose D = {1, 4, 9, 16, 25, 36} is the given set. This set contains 6 elements. The number of elements in set D is represented as n (D) and we can write it as n (D) = 6
Exercise
1.
Choose the correct alternative:
Which of the following is a set?
Days of the week
Happy people in your town
Easy problems from the book
Brilliant students in the school
If P represents the set of letters from the word ‘college’, then which of the following represents set P?