SQL related terms DCL,DML,DDl,TCL

1)DDL 
 
Data Definition Language (DDL) statements are used to define the database structure or schema. Some examples: 
CREATE - to create objects in the database
ALTER - alters the structure of the database
DROP - delete objects from the database
TRUNCATE - remove all records from a table, including all spaces allocated for the records are removed
COMMENT - add comments to the data dictionary
RENAME - rename an object

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2)  DML

Data Manipulation Language (DML) statements are used for managing data within schema objects. Some examples:
SELECT - retrieve data from the a database
INSERT - insert data into a table
UPDATE - updates existing data within a table
DELETE - deletes all records from a table, the space for the records remain
MERGE - UPSERT operation (insert or update)
CALL - call a PL/SQL or Java subprogram
EXPLAIN PLAN - explain access path to data
LOCK TABLE - control concurrency

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3)  DCL

Data Control Language (DCL) statements. Some examples:
GRANT - gives user's access privileges to database
REVOKE - withdraw access privileges given with the GRANT command

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4)  TCL

Transaction Control (TCL) statements are used to manage the changes made by DML statements. It allows statements to be grouped together into logical transactions.
COMMIT - save work done
SAVEPOINT - identify a point in a transaction to which you can later roll back
ROLLBACK - restore database to original since the last COMMIT
SET TRANSACTION - Change transaction options like isolation level and what rollback segment to use

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Mathematical Pre-requisities

Set:-
           Set is a collection of object without repetition and each object of set is called element of a set example D={x/x is a day of week}
Properties
1) Empty set  - It contains no elements denoted by ∅ {}.
2) Subset -  Set A is subset of B if every element in set A is in B denoted as A ⊂ B.
3) Equal sets -Two sets are equal if A ⊂ B and B ⊂ A..
4) Power set -A is a power set if 2^A.Set of all subsets A
        For example if,
           A={1,2,3}
           2^A={ {∅},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3} }
          2³=8 elements.
5) Compliment A' such that A'={x/x ∉ A}.
6) Union - A U B is all the elements in set A and B.
7) Intersection -A ∩ B is the element s both which is in A  and also in B.
8) Cardinality is the number of sets.


Relation :-  A relation R in set S is collection of ordered pair of elements in S.
Properties :-
1) Reflexive  -R is reflexive in S if xRx ∀ (for all) x ∈ S.
2) Symmetric -R is symmetric in x if xRy ⇒ yRx
3) Transitivie - R is transitive in x if xRy and yRz ⇒xRz
4)Equivalence relation -If relation is all three reflexive,symmetric and transitive.