Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Two functions f: A → B and g: B → C can be composed to give a composition g o f. This is a function from A to C defined by (g o f)(x) = g(f(x))ExampleLet f(x) = x + 2 and g(x) = 2x + 1, find (f o g)(x) and (g o f)(x).Solution(f o g)(x) = f(g(x)) = f(2x + 1) = 2x + 1 + 2 = 2x + 3(g o f)(x) = g (f(x)) = g(x + 2) = 2 (x+2) + 1 = 2x + 5Hence, (f o g)(x) ≠ (g o f)(x)Some Facts about ... Read More
Let’s say we installed MySQL version is 8.0 on our Windows OS. The bin directory is present at the following location −C:\Program Files\MySQL\MySQL Server 8.0\binLet us check the location. The screenshot is as follows −These are the drives −Go to C: drive and click Program Files −Now, click “MySQL” and open the folder −After that, click the current MySQL version folder. For us, it is MySQL Server 8.0 −Inside the folder, you can easily locate the bin folder as shown in the following screenshot −
The rules of mathematical logic specify methods of reasoning mathematical statements. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. It has many practical applications in computer science like design of computing machines, artificial intelligence, definition of data structures for programming languages etc.Major CategoriesMathematical logics can be broadly categorized into three categories.Propositional Logic − Propositional Logic is concerned with statements to which the truth values, "true" and "false", can be assigned. The purpose is to analyse these statements either individually or in a composite manner.Predicate ... Read More
Let 'G−' be a simple graph with some vertices as that of 'G' and an edge {U, V} is present in 'G−', if the edge is not present in G. It means, two vertices are adjacent in 'G−' if the two vertices are not adjacent in G.If the edges that exist in graph I are absent in another graph II, and if both graph I and graph II are combined together to form a complete graph, then graph I and graph II are called complements of each other.ExampleIn the following example, graph-I has two edges 'cd' and 'bd'. Its complement ... Read More
Graph coloring is nothing but a simple way of labelling graph components such as vertices, edges, and regions under some constraints. In a graph, no two adjacent vertices, adjacent edges, or adjacent regions are colored with minimum number of colors. This number is called the chromatic number and the graph is called a properly colored graph.While graph coloring, the constraints that are set on the graph are colors, order of coloring, the way of assigning color, etc. A coloring is given to a vertex or a particular region. Thus, the vertices or regions having same colors form independent sets.Vertex ColoringVertex ... Read More
For this, you can use INSERT INTO….SELECT statement. Let us first create a table −mysql> create table DemoTabe1 (Marks int); Query OK, 0 rows affected (0.66 sec)Insert some records in the table using insert command −mysql> insert into DemoTabe1 values(68); Query OK, 1 row affected (0.18 sec) mysql> insert into DemoTabe1 values(89); Query OK, 1 row affected (0.14 sec) mysql> insert into DemoTabe1 values(99); Query OK, 1 row affected (0.17 sec) mysql> insert into DemoTabe1 values(39); Query OK, 1 row affected (0.11 sec) mysql> insert into DemoTabe1 values(49); Query OK, 1 row affected (0.12 sec)Display all records from the table ... Read More
Let 'G' be a connected graph with 'n' vertices and 'm' edges. A spanning tree 'T' of G contains (n-1) edges.Therefore, the number of edges you need to delete from 'G' in order to get a spanning tree = m-(n-1), which is called the circuit rank of G.This formula is true, because in a spanning tree you need to have 'n-1' edges. Out of 'm' edges, you need to keep 'n–1' edges in the graph.Hence, deleting 'n–1' edges from 'm' gives the edges to be removed from the graph in order to get a spanning tree, which should not form ... Read More
Let us first create a table −mysql> create table DemoTable719 (FirstNumber int, SecondNumber int); Query OK, 0 rows affected (0.57 sec)Insert some records in the table using insert command −mysql> insert into DemoTable719 values(20, 10); Query OK, 1 row affected (0.18 sec) mysql> insert into DemoTable719 values(500, 50); Query OK, 1 row affected (0.22 sec) mysql> insert into DemoTable719 values(400, 20); Query OK, 1 row affected (0.11 sec)Display all records from the table using select statement −mysql> select *from DemoTable719;This will produce the following output −+-------------+--------------+ | FirstNumber | SecondNumber | +-------------+--------------+ | 20 | ... Read More
The center of a tree is a vertex with minimal eccentricity. The eccentricity of a vertex X in a tree G is the maximum distance between the vertex X and any other vertex of the tree. The maximum eccentricity is the tree diameter. If a tree has only one center, it is called Central Tree and if a tree has only more than one centers, it is called Bi-central Tree. Every tree is either central or bi-central.Algorithm to find centers and bi-centers of a treeStep 1 − Remove all the vertices of degree 1 from the given tree and also ... Read More
For this, you can use a subquery. Let us first create a table −mysql> create table DemoTable618 ( StudentId int NOT NULL AUTO_INCREMENT PRIMARY KEY, StudentFirstName varchar(100) ); Query OK, 0 rows affected (1.45 sec)Insert some records in the table using insert command −mysql> insert into DemoTable618(StudentFirstName) values('David'); Query OK, 1 row affected (0.23 sec) mysql> insert into DemoTable618(StudentFirstName) values('Chris'); Query OK, 1 row affected (0.44 sec) mysql> insert into DemoTable618(StudentFirstName) values('Robert'); Query OK, 1 row affected (0.54 sec) mysql> insert into DemoTable618(StudentFirstName) values('Sam'); Query OK, 1 row affected (0.24 sec) mysql> insert into DemoTable618(StudentFirstName) values('Mike'); Query OK, 1 ... Read More