Mathematics

 The relation is an association between two or more things. relation between sets is the association between then that defines how the sets are related.  Types of relations: Reflexive relation If a set A have elements like {a,b,c,d} the relation, must contain all (a,a), (b,b),(c,c),(d,d) in it then the relation is called as reflexive relation. in simple words the relation which contain (a,a) pair for all a n=belongs to the set, then the relation  on the set is called as reflexive relation. each element present in the set must be related to it self then the relation is called as reflexive relation. for example: A={1,2,3,6,8} the relation on set A is such that it defines (a,b) belongs to A when b is divisible by a. here R={(1,1),(1,2),(1,3),(1,6),(1,8),(2,2),(2,6),(2,8),(3,3),(3,6),(6,6),(8,8)}  here in the above relation all pairs that are like (a,a) are present in relation R that are: (1,1),(2,2),(3,3),(6,6),(8,8) all are present in the relation set so the above rela...

  directed graph A graph of the given relation. Let A and B are the two finite sets and R is the relation from A to B. For a graphical representation of a relation on a set is represented by a point. Each element in a set is represented by a point in diagraph. Those points are called as nodes. An edge is drawn from one point to another related point. This edges are called as arc. The direction in the diagraph is represented by an arrow. And all arrows in directed graph with atrows called as directed arcs. For example: Draw a  directed graph that represents the relation: R={(1,1),(2,2),(1,2),(2,3),(3,2),(3,1),(3,3)} The loops present in the diagraph represents the reflexive property that are (1,1),(2,2),(3,3) the edge from 1 to 2 represents (1,2) and similarly other edges are shown. Hasse diagram  Hasse diagram is a diagram which represents partial ordered set in the form of graph without showing its transitive relation. Steps to draw a Hasse diagram: Start with a directed...