Discrete Structures Question Paper of 3rd Semester CSE74 Download Previous Years Question Paper 1

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December-2002
CS-203/204
DISCRETE STRUCTURES
B.Tech. 3rd Semester-212
Note: Section –A is compulsory. Attempt any four question from section-B.A attempt any two questions from section –C.
Section –A
1.
a.     Show that we can have AB = AC. Without B=C
b.     Prove that AB = BA.
c.      Explain the principle of duality.
d.     Find the number of relations from A ={a,b,c} to B = {a,2}
e.      Define the recurrence relation.
f.       Find the formula for the inverse of (x) = x2- 1.
g.     Define multigraph
h.     What is in degree and out degree of a graph?
i.       Show that the identity element in a group G is unique.
j.       Define normal subgroup of a group G.

Section –B

2.     Suppose g(t)= t3-2t2-6t-3, find the roots of g(t), assuming g(t) has an integral root.

3.     Show that the relation of being associate is an equivalence relation in a ring R

4.     Define a rooted tree T with an example and show how it may be viewed as directed graph.
5.     Mention the properties of minimum spanning trees.

6.     Let G be any group and let a be any element of  define the cyclic group generated by a.

Section-C

7.     If H is a subgroup of G, show that HH = H.

8.     Suppose J is an ideal in commutative ring R, show that R/J is commutative.

9.     Prove : A function f: A →   B has an inverse if f is objective