Relations may exist between objects of the same set or between objects of two or more sets.Definition and PropertiesA binary relation R from set x to y (written as xRy or R(x, y)) is a subset of the Cartesian product x × y. If the ordered pair of G is ... Read More

Predicate Calculus deals with predicates, which are propositions containing variables.PredicateA predicate is an expression of one or more variables defined on some specific domain. A predicate with variables can be made a proposition by either assigning a value to the variable or by quantifying the variable.Consider the following statement.Ram is ... Read More

Power set of a set S is the set of all subsets of S including the empty set. The cardinality of a power set of a set S of cardinality n is 2n. Power set is denoted as P(S).Example −For a set S = { a, b, c, d } ... Read More

Planar graph − A graph G is called a planar graph if it can be drawn in a plane without any edges crossed. If we draw graph in the plane without edge crossing, it is called embedding the graph in the plane.Non-planar graph − A graph is non-planar if it ... Read More

A graph 'G' is said to be planar if it can be drawn on a plane or a sphere so that no two edges cross each other at a non-vertex point.ExampleRegionsEvery planar graph divides the plane into connected areas called regions.ExampleDegree of a bounded region r = deg(r) = Number ... Read More

Pendent VertexBy using degree of a vertex, we have a two special types of vertices. A vertex with degree one is called a pendent vertex.ExampleHere, in this example, vertex 'a' and vertex 'b' have a connected edge 'ab'. So with respect to the vertex 'a', there is only one edge ... Read More

Partition of a set, say S, is a collection of n disjoint subsets, say P1, P1, ... Pn that satisfies the following three conditions −Pi does not contain the empty set.                        [ Pi ≠ { ∅ } for all ... Read More

A spanning tree with assigned weight less than or equal to the weight of every possible spanning tree of a weighted, connected and undirected graph $G$, it is called minimum spanning tree (MST). The weight of a spanning tree is the sum of all the weights assigned to each edge ... Read More

A graph can be represented using Adjacency Matrix way.Adjacency 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 and A[Vy][Vx]=1, otherwise ... Read More

Mathematics can be broadly classified into two categories −Continuous Mathematics − It is based upon continuous number line or the real numbers. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. For example, a function in continuous mathematics can ... Read More