Sets JEE Main PYQ #sets #setsrelationsandfunctions #setsandrelations

Sets JEE Main PYQ #sets #setsrelationsandfunctions #setsandrelations
@Quick Maths
A set is a collection of distinct objects, considered as an object in its own right. In mathematics, sets are used to group elements that share common characteristics. These elements can be anything: numbers, letters, or even other sets.

Key characteristics of sets:

Notation: Sets are usually written in curly braces {}. For example, a set of numbers from 1 to 5 is written as
A={1,2,3,4,5}.
Elements: The objects in a set are called elements or members. An element can belong to a set or not. For example, 2 is an element of the set
A={1,2,3}, but 4 is not.
Distinctness: Each element in a set is unique; there are no duplicates in a set. So, the set
{1,2,2,3} is equivalent to
{1,2,3}.
Order: The order of elements in a set does not matter. Thus,
{1,2,3} is the same as
{3,2,1}.
Types of sets:

Finite Set: A set with a limited number of elements, like
A={1,2,3}.
Infinite Set: A set with an unlimited number of elements, like the set of all natural numbers
N={1,2,3,4,…}.
Subset: A set
𝐴
A is a subset of set
𝐵
B if every element of
A⊆B.
Universal Set: The set that contains all elements under consideration, often denoted as
𝑈

Empty Set: A set that contains no elements, denoted as

∅.
Power Set: The set of all subsets of a set
𝐴
A, denoted as

P(A).
Disjoint Sets: Sets that have no elements in common.
Operations on Sets:

Union: The set containing all elements from both sets, denoted as

A∪B.
Intersection: The set of elements common to both sets, denoted as

A∩B.
Difference: The set of elements in
A−B.
Complement: The set of elements not in set
𝐴
A, relative to a universal set
𝑈
U, denoted
U−A.
Venn Diagrams: Venn diagrams are often used to visually represent sets and their relationships through circles or other shapes.