CALCULUS: CHAPTER 01 SETS
SET: A WELL DEFINED COLLECTION OF OBJECTS
Set is the very first chapter of class 11 maths syllabus. It is also the beginning of calculus. Set is like a building block for subjects like calculus and linear algebra. Set theory has a wide variety of use in different subjects like physics. Set was developed by George Boole and George F. L. P. Cantor in the late 19th century.
According to CBSE (central Board Of Secondary Education) curriculum in India Set Theory is introduced in Class 11. NCERT publication brings compact and accurate books based on the cbse pattern. As I mentioned earlier Set is the building block of calculus. So we are going to focus on Set and understand this very carefully.
The topics we are going to cover under this section are:
- Sets
- Subsets
- Venn Diagram
- Operation On Sets
- Compliment of a Set
- Practical problems on Union and Intersection of two Sets
We will study all topics of Set based on class 11 syllabus. There will be 20-25 min lectures covering all topics necessary for understanding Sets.
CALCULUS | C01L01 | INTRODUCTION TO SETS
The first lecture covers the “introduction of Set” dealing the following:
- What is Set?
- Examples on Set
- Representation of Set
- Roster Method
- Set-builder Method
- Finite Set
- Infinite Set
- Null Set/ Empty Set/ Void Set
- Singleton Set
CALCULUS | C01L02 | SUBSETS & UNIVERSAL SET
The second lecture covers the following:
- Subsets
- Superset
- Symbolic definition of Subset
- Equality of Sets using subsets concept
- Understanding Rational numbers as a subset
- Number of subsets of a given Set
- Intervals as a subset of R
- Power Set
- Universal set
CALCULUS | C01L03 | OPERATIONS ON SETS
The third lecture on “operation on sets” covers the following:
- Venn Diagram
- Union of Sets
- Intersection of Sets
- Difference of Sets
- Complement of a Set
CALCULUS | C01L04 | PRACTICAL PROBLEMS ON SETS
The fourth lecture on “practical problems on sets” covers the following:
- Cardinal Number of a Set
- n(AUB) | When Sets are Disjoint
- n(AUB) | When Sets are not Disjoint
- n(AUBUC) | When Sets are not Disjoint
- Example 1 – A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports. Then the number of students who received medals in exactly two of the three sports?
- Example 2 -In a survey of 100 persons, it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazine A and C, 5 read magazine B and C and 3 read all the three. How many read none of the magazine?
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