## Discrete Mathematics pdf Notes – DM pdf Notes file

Discrete Mathematics pdf Notes – DM pdf Notes – DM pdf Notes file to download are listed below please check it –

Note :- These notes are according to the R09 Syllabus book of JNTU.In R13 and R15,8-units of R09 syllabus are combined into 5-units in R13 and R15 syllabus. If you have any doubts please refer to the JNTU Syllabus Book.

**Unit-1:**

- Logic and proof,propositions on statement,connectives,basic connectives,truth table for basic connectives,And,
- Disjunction,conditional state,bi conditional state,tautology,contradiction,fallacy,contigency,logical equialances,idempotent law,
- associtative law,commutative law,demorgans law,distributive law,complements law,dominance law,identity law.
- A praposition of on statement is a declarative sentence which either true (or) false not both,conective is an operation which is used to connect two (or) more than two statements.simple is called sentencal connective.

**Unit-2:**

- Combinatorics,strong induction,pigeon hole principle,permutation and combination,reccurence relations,linear non homogeneous reccurrence relation with constant,the principle of inclusion and exclusion.

**Unit-3:**

- Graphs,parllel edges,adjecent edges and vertices,simple graph,isolated vertex,directed graph,undirected graph,mixed graph,multigraph,pseduo graph,degree,
- in degree and outdegree,therom,regular graph,complete graph,complete bipartite,subgraph,adjecent matrix of a simple graph,incidence matrix,path matrix,
- graph isomorphism,pths,rechabality and connected path,length of the path,cycle,connected graph,components of a graph,konisberg bridge problem,Euler parh,euler circuit,
- hamiltonian path,hamiltonian cycle.if two edges have same end points,then the edges are called parllel edges.two edges are called as adjecent if they are incident in a common vertex.
- two vertices are said to be adjecent if they are the end points of any one edge.a graph which has neither self loops nor parllel edges is called simple.A graph in which every edge is directed is called digraph.
- A graph in which every edge is undirected is called undirected graph.

**Unit-4:**

- Alebric structers,properties,closure,commutativity,associativity,identity,inverse,distributive law,inverse element,notation,semi group,monoid,cycle monoid,
- morphisms of semigrouphs,morpism of monoids,groups,abelian group,order of group,composition table,properties of groups,subgroups,kernal of a elomorphism,isomorphism,
- cosets,lagranges therom,normal subgroups,natural homomorphism,rings,field.

**Unit-5:**

- lattices and boolean algebra,reflexive,symmetric,transitive,antisymmetric,equivalance relation,poset,hane diagram,propertie of lattices,idempolent law,commutative law,associative law,absorbtion law,boolean algebra.