Discrete Structures Question Paper of 3rd Semester CSE74 Download Previous Years Question Paper 13

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Total No. of Questins:9]

May-2003

DISCRETE STRUCTURES

SUBJECT CODE : CS - 203

B.Tech. (Sem. – 3^{rd -} 2053)

Time : 03 Hours

Note : Section –A 9 compulsory. Attempt any Four questions form section –B. Attempt any two questions from Section-C.

Section-A

1.       

a.     If A and B are disjoint sets, prove that: n(AUB) =n(A)+(B)

b.     Show that p↔ q logically imply p→ q.

c.      Define trivial graph

d.     Define  degree in graph.

e.      Define closed path and cycle in a graph.

f.       Define ad abelain group.

g.     Define group Homomorphism.

h.     Define group Isomorphism.

i.        Define normal subgroup of a group.

j.       Differentiate between an ordered and unordered partition of a finite set.

Section –B

2.     Let H be a subgroup of G. define a coset representative system for H in G.

3.     Prove that an undirected graph G possesses an Eulerian circuit if it is connected and all its vertices are of even degree.

4.     Suppose a graph G contains two distinct path from a vertex a to b. show that G has a cycle.

5.     Define the term injective, surjective and bijetive with example.

6.     Find the generating function of the Fibonacci sequence.

Section –C

7.   

Show that D is isomorphic to the complex number C whence D is field.

8.     Suppose a directed graph G has m vertices. Show that if there is a path P from vertex u to v, then there is a path P of length m-1 or less form u to v.

9.     Show that how the set options of  union and intersection defined classes of sets .