Dr Bhim Rao Ambedkar University 2006 B.Tech Information Technology Discrete Mathmatical structure - Question Paper

Y-308
SECOND YEAR OF COMPUTER SCIENCE AND ENGINEERING (PART-1) EXAMINATION, 2006

DiscRETE MATHEMATICAL STRUCTURE
Total Marks: 100
Time: 3.00p.m. To 6.00p.m.

Instructions: 1) Attempt any 3 ques. from every part.

2) Figures to right indicate full marks.


SECTION-1

Q.1 a) indicates the subsequent implications:[Marks 8=4*2]


1) (P IMPLIES Q) IMPLIES Q = P OR Q

2) ((P OR ~P) IMPLIES Q) IMPLIES ((P OR ~P) IMPLIES R)=(Q IMPLIES R)


b) Draw the Hasse diagram of the subsequent sets under the partial ordering relation ’divides’.[Marks 8]

1) {1, 2, 3, 6, 12}

2) {3, 9, 27, 54}



Q.2 a) what is monoid? describe the subsequent with respect to monoids.[Marks 8=2*4]


1. Homomorphism

2. Isomorphism

3. Monomorphism


Q.3 Write a short notes on:[Marks 18=6*3]

1) Partitions and covering of set

2) POSET and Hasse diagram

3) Normal and principal normal forms

Q.4 Write a short notes on:[Marks 16=8*2]

1) Algebraic systems

2) Normal and principal normal forms

SECTION-2



Q.5 a) describe the lattices as a POSET. describe greatest lower bound and lowest upper bound with examples.[Marks 8]

b) describe group. describe and provide examples of various kinds of groups.[Marks 10]


Q.6 a) discuss about the recovery of single fault in group codes.[Marks 8]

b) discuss the linked representation of binary tree.[Marks 8]

Q.7 a) discuss the inorder traversal algorithm for the tree structure. [Marks 8]

b) For the Boolean function F=XYZ+XYZ+XYZ provide the subsequent representations:[Marks 8=2*4]

1. Circuit diagram

2. The table

3. Truth table

4. K-map


Q.8 a) derives the reverse polish expression for the subsequent expressions: :[ Marks 8=4*2]

1) a + (b/c) *d

2) (a + b) (c + d/e) * f


b) What is diagraph? describe the following:[Marks 8]

1. asymmetric diagraph

2. converse of a diagraph

3. reflexive diagraph

Earning:   Approval pending.