Maths Class 11 Chapter 2 Notes
Handwritten notes on Maths Class 11 Chapter 2 Notes of Sets, Functions, and Groups written by Professor M. Asad Khalid Suib. These notes are very helpful in the preparation of Sets Functions and Groups Notes for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Our comprehensive Maths Class 11 Chapter 2 Notes will ensure you're fully prepared for your exams.
- Definition of a set with examples
- Definition of members with examples
- Definition of order of set with examples
- Definition of singleton set with examples
- Definition of an empty set with examples
- Definition of equal sets with examples
- Definition of equivalent sets with examples
- Definition of a subset with examples
- Definition of a proper subset with examples
- Definition of an improper subset with examples
- Definition of finite or infinite subsets with examples
- Complete Solutions of each question of Exercise 2.1
- Definition of union of two sets with its symbolically and examples
- Definition of Intersection of two sets with its symbolically and examples
- Definition of disjoint sets with examples
- Definition of overlapping sets with examples
- Definition of a complement of a set with its symbolically and examples
- Definition of difference of two sets with its symbolically and examples
- Complete Solutions of each question of Exercise 2.2
- Definition of induction and Deduction
- Important points and Aristotlian Logics and non-Aristotlian Logics
- Definition of proposition definition of negation and truth table.
- Definition of proposition definition of negation and truth table
- Definition of disjunction and truth table
- Implication orconditional with its truth table
- Definition of Tautologies with examples
- Definition of Absurdity with examples
- Definition of Contingency with examples
- Complete Solutions of each question of Exercise 2.4
- Complete Solutions of each question of Exercise 2.5
- Definition of binary relation with its notation.
- Definition of domain and range
- Definition of function and its types into function, Onto function (surjective) function, 1-1 and into (injective) function, 1-1 and onto function (bijective) function, linear function, quadratic function, inverse of each function.
- Complete Solutions of each question of Exercise 2.6
- Definition of groupoid,Semi group
- Complete Solutions of each question of Exercise 2.8
- Solution of all examples in this chapter.
- We are familiar with the notion of a set since the word is frequently used in everyday speech, for instance, water set, tea set, sofa set. It is a wonder that mathematicians have developed this ordinary word into a mathematical concept as much as it has become a language which is employed in most branches of modern mathematics. For the purposes of mathematics, a set is generally described as a well-deined collection of distinct objects. By a well-deined collection is meant a collection, which is such that, given any object, we may be able to decide whether the object belongs to the collection or not. By distinct objects we mean objects no two of which are identical (same). The objects in a set are called its members or elements. Capital letters A, B, C, X, Y, Z etc., are generally used as names of sets and small letters a, b, c, x, y, z etc., are used as members of sets. There are three diferent ways of describing a set
- i) The Descriptive Method: A set may be described in words. For instance, the set of all vowels of the English alphabets.
- ii) The Tabular Method: A set may be described by listing its elements within brackets. If A is the set mentioned above, then we may write: A = {a,e,i,o,u}.
- iii) Set-builder method: It is sometimes more convenient or useful to employ the method of set-builder notation in specifying sets. This is done by using a symbol or letter for an arbitrary member of the set and stating the property common to all the members. Thus the above set may be written as: A = { x |x is a vowel of the English alphabet} This is read as A is the set of all x such that x is a vowel of the English alphabet. The symbol used for membership of a set is U . Thus a U A means a is an element of A or a belongs to A. c ∉ A means c does not belong to A or c is not a member of A. Elements of a set can be anything: people, countries, rivers, objects of our thought. In algebra we usually deal with sets of numbers. Such sets, alongwith their names are given below:-
- N = The set of all natural numbers = {1,2,3,...}
- W = The set of all whole numbers = {0,1,2,...}
- Z = The set of all integers = {0,±1,+2....}.
- Z ‘ = The set of all negative integers = {-1,-2,-3,...}.