Review Note

⭐Set
➤Types of Set

⭐Set:
➤A well defined and distinct collection of object.
➤Each object must be different.
➤Each object has to fit into the required well-defined condition.

❖  Types of set:
1. Finite Set
2. Infinite Set
3. Singleton Set
4. Null Set / Empty Set
5. Equivalent Set = Sets having same number of elements / same cardinality

➤Cardinal Number = Number of elements in a set. ex - n(A) = 5, n(B) = 4, n(C) = 3 
A={1,2,3} and B={2,3,4}
n(A) = n(B)
➤Sp, Cardinality = Size

6. Equal Sets:

➤Equivalent Set
➤Precisely Same Elements

➤A={1,2,3} and B={2,3,4}

➤So, n(A) != n(B)

❖  Number of subsets of a set = 2^{n
Where n is the cardinality of A.}
7. Proper Set: Missing at least one element from the original set.
➤At least one element of A.
❖  Every set is a subset of itself.

8. Superset
➤A is a superset of B

9. Trivial Set
➤Null Set and the set itself 

➤Number of Subsets of a set A : \(2^n\) 
where, n is the cardinality of A.
➤Number of proper subsets of A : 
\(2^n -1\)