The document defines some basic concepts of sets including: - A set is a well-defined collection of objects that can be represented in statement, roster, or set-builder form. - Standard sets in math include the sets of natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. - An element belongs to a set if it is contained within the set. Sets are usually represented by capital letters and elements by lowercase letters. - Sets can be empty, equal, equivalent, finite or infinite, singleton, subsets of other sets, or universal sets containing all elements of other sets.

1. SIMPLE CONCEPTS OF SETS
SIR ABDUL GHAFFAR
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SOLUTION

2. a set is defined as a well-defined collection of
objects
Example
Some standard sets in maths are:
•Set of natural numbers, ℕ = {1, 2, 3, ...}
•Set of whole numbers, W = {0, 1, 2, 3, ...}
•Set of integers, ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}
•Set of rational numbers, ℚ = {p/q | q is an integer and q ≠ 0}
•Set of irrational numbers, ℚ' = {x | x is not rational}
•Set of real numbers, ℝ = ℚ ∪ ℚ'
Sets

3. If ‘A’ is a set and ‘a’ one of its elements then: ‘
a ∈ A’ denotes that element ‘a’ belongs to ‘A’ whereas,
‘a ∉ A’ denotes that ‘a’ is not an element of A.
Alternatively, we can say that ‘A’ contains ‘a’. A set is
usually represented by capital letters and an element of the
set by the small letter.
How to denote Sets?

4. There are mainly 3 ways to represent a set:
Statement form : Here, a single statement describes all the elements inside a set.
For example: V = The set of all vowels in English.
Roaster form (tabular method) : In this form all the members of the given set are
enlisted within a pair of braces { }, separated by commas.
For example: E = {2, 4, 6, 8, 10}
Set Builder form : Here, a property is stated that must be common to all the elements of
that particular set.
For Example N = { x : x is positive integers between 10 to 20 }
We read the set builder form as ” N is the set of all x such that x is a positive integer between
10 to 20″. Braces{} denote the set while ‘:’ denotes ‘such that’.
Representation of Sets

5. Empty Set : A set with no elements. Empty sets are also called null sets or void sets and are
denoted by { } or Φ.
Equal Sets : Sets with equal elements.
 Example: A = {5, 6, 7} and B = {5, 6, 5, 7, 7}.
 Here, the elements of A and B are equal to each other (5, 6, 7) i. e., A = B
In case of repetition as in B we write B = {5, 6, 7} by ignoring the repetition.
Types of Sets

6. Equivalent Sets : Sets with the equal number of members.
 Ex. A = {3, 6, 8} and B = {p, q, r}.
 Both A and B having three elements are equivalent sets.
Finite and Infinite Sets : Based on the number of elements (finite or
infinite) present in the set, the set is either finite or infinite. In case of infinite
the set, it is given as:
 N = Numbers divisible by 2 = {2,4, 8, 12, 16…..}
Singleton Set : A set with a single element. For example, {9}.

7. Subsets: A set ‘A’ is said to be a subset of B if each element of A
is also an element of B.
For Example: A={1,2}, B={1,2,3,4}, then A ⊆ B
Universal Set: A set which consists of all elements of other sets .
For Example : A={1,2}, B={2,3}, The universal set here will be, U =
{1, 2,3}

8. Thank you