Discrete Mathematics

(a) Show that the relation $a\le b$ on a set A = {1, 2, 3, 4} is reflexive. (b) Show that the relation on R defined by $aRb$ if and only if $a<b$ is not reflexive.

What do you understand by Ring-sum of two graph?

What is Injective mapping?

Define Incidence matrix.

Differentiate between Universal relation and Identify relation.

How many kinds of functions are there? Name them.

What are the properties of subset?

Find the difference of the following two graphs $G_1$ and $G_2$.

Draw the diagram of the graph obtained by the fusion of the vertices c in the following graph G.

Obtain CNF of $p\wedge (p\to q)$.

Find the number of paths of length 3 between two vertices of $K_4$.

Briefly describe Kruskal's algorithm.

Using Warshall's algorithm, find the transitive closure of the relation R = {(a, a), (a, b), (a, d), (c, b), (c, c), (d, b), (d, c), (d, d)} on {a, b, c, d}

Define Algebraic Structure and their properties.

Briefly describe Prim's algorithm.

Explain Semi Graph, Monoid Group and Abelian Group.

Draw the graph represented by the following incidence matrices.

Find the incidence matrices for the following graphs $G_1$ and $G_2$.

Find the adjacency matrices of the following graphs.

Explain Pigeonhole principle.

Name types of sets. Explain each type of set.

Explain Warshall's Algorithm.

Obtain the PDNF of the proposition $\neg (p\vee q)\leftrightarrow (p\wedge q)$.

Differentiate between Eulerian and Hamiltonian Path and Circuit with diagram.

Find the DNF of ($\neg p\to r$) ∧ ($p\leftrightarrow q$) using truth table.