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Mahesh Parahar has Published 191 Articles

Mahesh Parahar
15K+ Views
Lazy and Eager are two types of data loading strategies in ORMs such as hibernate and eclipse Link. These data loading strategies we used when one entity class is having references to other Entities like Employee and Phone (phone in the employee). Lazy Loading − Associated data loads only when we ... Read More

Mahesh Parahar
687 Views
The Empty Relation between sets X and Y, or on E, is the empty set ∅The Full Relation between sets X and Y is the set X × YThe Identity Relation on set X is the set { (x, x) | x ∈ X }The Inverse Relation R' of a ... Read More

Mahesh Parahar
5K+ Views
To deduce new statements from the statements whose truth that we already know, Rules of Inference are used.What are Rules of Inference for?Mathematical logic is often used for logical proofs. Proofs are valid arguments that determine the truth values of mathematical statements.An argument is a sequence of statements. The last ... Read More

Mahesh Parahar
636 Views
If G = (V, E) be a non-directed graph with vertices V = {V1, V2, …Vn} thenn ∑ i=1 deg(Vi) = 2|E|Corollary 1If G = (V, E) be a directed graph with vertices V = {V1, V2, …Vn}, thenn ∑ i=1 deg+(Vi) = |E| = n ∑ i=1 deg−(Vi)Corollary 2In ... Read More

Mahesh Parahar
2K+ Views
German mathematician G. Cantor introduced the concept of sets. He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or descriptions.Set theory forms the basis of several other fields of study like counting theory, relations, graph theory, and finite state ... Read More

Mahesh Parahar
9K+ Views
Venn diagram, invented in 1880 by John Venn, is a schematic diagram that shows all possible logical relations between different mathematical sets.ExamplesSet OperationsSet Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product.Set UnionThe union of sets A and B (denoted by A ∪ B) is ... Read More

Mahesh Parahar
2K+ Views
To deduce new statements from the statements whose truth that we already know, Rules of Inference are used.What are Rules of Inference for?Mathematical logic is often used for logical proofs. Proofs are valid arguments that determine the truth values of mathematical statements.An argument is a sequence of statements. The last ... Read More

Mahesh Parahar
5K+ Views
Rooted TreeA rooted tree G is a connected acyclic graph with a special node that is called the root of the tree and every edge directly or indirectly originates from the root. An ordered rooted tree is a rooted tree where the children of each internal vertex are ordered. If ... Read More

Mahesh Parahar
2K+ Views
A relation can be represented using a directed graph.The number of vertices in the graph is equal to the number of elements in the set from which the relation has been defined. For each ordered pair (x, y) in the relation R, there will be a directed edge from the ... Read More

Mahesh Parahar
1K+ Views
There are mainly two ways to represent a graph −Adjacency MatrixAdjacency ListAdjacency MatrixAn Adjacency Matrix A[V][V] is a 2D array of size V × V where $V$ is the number of vertices in a undirected graph. If there is an edge between Vx to Vy then the value of A[Vx][Vy]=1 ... Read More