1st Year Math Notes Chapter 2
Handwritten notes on 1st Year Math Notes Chapter 2 of Sets, Functions, and Groups written by Professor M. Sulman Sherazi Suib. These notes are very helpful in the preparation of Sets Functions and Groups 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 1st Year Math Notes Chapter 2 will ensure you're fully prepared for your exams.
- Definition of a set with its examples and how many ways to describing a set (i) descriptive method (ii) tabular method (iii) set-builder method
- Kinds of a set order of a set with examples singleton set with examples finite set with examples infinite set with examples equal sets with examples one-to-one correspondence with examples equivalent sets with examples subset with examples in a proper set with examples in-proper set with examples of power set with examples and Universal Set with examples.
- Operations on Sets with examples Intersection of two sets with examples of disjoint sets with examples complement sets of assets with examples overlapping sets with examples difference of two sets with examples Venn diagrams
- De Morgan's Laws with examples
- Definition of induction definition of deduction definition of preposition definition of conjunction definition of inflection or conditional conditionals related with a given condition.
- Definition of Quantifiers and their two quantifiers (i) Universal (ii) Existential
- Into Function Onto (Surjective) Function one-to-one and Injective Fuction Set Builder Notation for a function with examples.
- What is the binary operations and property of binary operations with examples?
- Definition of groups group void with examples semi groups with examples available in group with examples of finite group with examples infinite group with examples monohydrate group with examples group with examples.
- Questions with their solutions of exercises 2.1 , 2.2 ,2.3,2.4,2.5,2.6,2.7,2.8 Complete solution of the definitions, examples, and exercises solutions. Universal Set: When we are studying any branch of mathematics the sets with which we have to deal, are generally subsets of a bigger set. Such a set is called the Universal set or the Universe of Discourse. At the elementary level when we are studying arithmetic, we have to deal with whole numbers only. At that stage the set of whole numbers can be treated as Universal Set. At a later stage, when we have to deal with negative numbers also and fractions, the set of the rational numbers can be treated as the Universal Set.
- Which of the following sets are inite and which of these are ininite? i) The set of students of your class. ii) The set of all schools in Pakistan. iii) The set of natural numbers between 3 and 10. iv) The set of rational numbers between 3 and 10. v) The set of real numbers between 0 and 1. vi) The set of rationales between 0 and 1. vii) The set of whole numbers between 0 and 1 viii) The set of all leaves of trees in Pakistan. viii) {5, 10, 15,.....,55555}, {5, 10, 15, 20,....... }.
- Venn diagrams are very useful in depicting visually the basic concepts of sets and relationships between sets. They were irst used by an English logician and mathematician John Venn (1834 to 1883 A.D). In a Venn diagram, a rectangular region represents the universal set and regions bounded by simple closed curves represent other sets, which are subsets of the universal set. For the sake of beauty these regions are generally shown as circular regions. In the adjoining igures, the shaded circular region represents a set A and the remaining portion of rectangle representing the universal set U represents A’ or U - A.
- Since the empty set contains no elements, therefore, no portion of U represents it. If in the diagrams given on preceding page we replace B by the empty set (by imagining the region representing B to vanish).