NEET (2024 Updated)-National Eligibility cum Entrance Test (Medical) Chemistry Coaching Programs
📹 Video Course 2024 (8 Lectures [4 Hrs : 33 Mins]): Offline Support
Click Here to View & Get Complete Material
Rs. 100.00
1 Month Validity (Multiple Devices)
⏳ 🎯 Online Tests (5 Tests [50 Questions Each]): NTA Pattern, Analytics & Explanations
Click Here to View & Get Complete Material
Rs. 500.00
3 Year Validity (Multiple Devices)
🎓 Study Material (159 Notes): 2024-2025 Syllabus
Click Here to View & Get Complete Material
Rs. 350.00
3 Year Validity (Multiple Devices)
🎯 3111 MCQs (& PYQs) with Full Explanations (2024-2025 Exam)
Click Here to View & Get Complete Material
Rs. 650.00
3 Year Validity (Multiple Devices)
NCERT Class 11- Math՚s Exemplar Chapter 1 Sets CBSE Board Problems
Overview
This chapter deals with the concept of a set, operations on sets. Concept of sets will be useful in studying the relations and functions.
Set and their representations: A set is a well-defined collection of objects. There are two methods of representing a set
(i) Roaster or tabular form
(ii) Set builder form
The empty set:
A set which does not contain any element is called the empty set or the void set or null set and is denoted by {} or .
Finite and infinite sets:
A set which consists of a finite number of elements is called a finite set otherwise, the set is called an infinite set.
Subsets:
A set A is said to be a subset of set B if every element of A is also an element of B. In symbols we write .
We denote
Set of real numbers byR
Set of natural numbers byN
Set of integers byZ
Set of rational numbers byQ
Set of irrational numbers byT
We observe that
Equal sets:
Given two sets A and B, if every elements of A is also an element of B and if every element of B is also an element of A, then the sets A and B are said to be equal. The two equal sets will have exactly the same elements.
Intervals as subsets of R: Let and . Then
(a) An open interval denoted by (a, b) is the set of real numbers
(b) A closed interval denoted by [a, b] is the set of real numbers
(c) Intervals closed at one end and open at the other are given by
Power set:
The collection of all subsets of a set A is called the power set of A. It is denoted by . If the number of elements in A = n , i.e.. , n (A) = n, then the number of elements in .
Universal set
This is a basic set; in a particular context whose elements and subsets are relevant to that particular context. For example, for the set of vowels in English alphabet, the universal set can be the set of all alphabets in English. Universal set is denoted byU.
Venn Diagrams
Venn Diagrams are the diagrams which represent the relationship between sets. For example, the set of natural numbers is a subset of set of whole numbers which is a subset of integers. We can represent this relationship through Venn diagram in the following way.
Union of Sets:
The union of any two given sets A and B is the set C which consists of all those elements which are either in A or in B. In symbols, we write
Some properties of the operation of union.
(i)
(ii)
(iii)
(iv)
(v)