## Summary

*This chapter deals with some basic definitions and operations involving sets. These are summarised below:*

*A set is a well-defined collection of objects. **A set which does not contain any element is called *empty* set. **A set which consists of a definite number of elements is called finite set, otherwise, the set is called infinite set.**Two sets A and B are said to be equal if they have exactly the same elements. **A set A is said to be *subset* of a set *B,* if every element of A is also an element of B. Intervals are subsets of R.**A power set of a set A is *collection* of all subsets of A. It is denoted by P(A).**The union of two sets A and B is the set of all those elements which are either in A or in B.**The intersection of two sets A and B is the set of all elements which are common. The difference of two sets A and B in this order is the set of elements which belong to A but not to B.**The complement of a subset A of universal set U is the set of all elements of U which are not the elements of A.**For any two sets A and B, (*A ∪ B*)′ = A′ ∩ B′ and ( *A ∩ B* )′ = A′ ∪ B′ **If A and B are finite sets such that *A ∩ B* = φ, then n (*A ∪ B*) = n (A) + n (B). If *A ∩ B* ≠ φ, then n (*A ∪ B*) = n (A) + n (B) – n (*A ∩ B*)*

## Lecture - 1

- Meaning of Sets
- Roster form (Listing Method)
- Set builder form (Property Method)
- Belongs to
- Empty Set (Null Set) (Void Set)
- Finite Set
- Infinite Sets
- NCERT Exercise 1.1
- NCERT Exercise 1.2

## Lecture - 2

- Subsets
- Difference between subset and belongs to
- Power Set
- Represent Real Numbers through closed and open intervals
- NCERT Exercise 1.3

## Lecture - 3

- Union operation on Sets
- Properties of Union
- Intersection operation on Sets
- Properties of Intersection
- Disjoint Sets
- Subtraction operation on Sets
- NCERT Exercise 1.4

## Lecture - 4

- Complement of Sets
- Properties of Complement
- Venn Diagrams
- NCERT Exercise 1.5

## Lecture - 5

- Cardinality of Sets
- NCERT Exercise 1.6
- NCERT Examples
- NCERT Miscellaneous Exercise