Shivaji University 2005 B.E Computer Science DMS - Question Paper

Y-308
SECOND YEAR OF COMPUTER SCIENCE AND ENGINEERING (PART-1) EXAMINATION, 2005
SHIVAJI UNIVERSITY, KOLHAPUR
DiscRETE MATHEMATICAL STRUCTURE

Day and Date: Wednesday, 30-05-2005 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) describe atomic statement. provide examples.[Marks 4]


b) What is connectivity? describe various basic connectives.[Marks 6]


c) describe and provide the truth table for the subsequent.[Marks 6=2*3]

1. Bidirectional

2. Conjunction

3. Conditional



Q.2 a) provide principle conjunctive disjunctive normal forms.[Marks 8=4*2]


1) (P AND Q) OR (~P AND R) OR (Q AND R)


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


b) describe a void relation in set X. provided set S = {1,2,3,……….10} and relation R on S where R={(x, y) | x + y=10}.Give the properties of R.[Marks 10]


Q.3 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.4 a) what is monoid? describe the subsequent with respect to monoids.[Marks 8=2*4]


1. Homomorphism

2. Isomorphism

3. Monomorphism


b) What is function? provide various kinds of functions with suitable example.[Marks 8]



Q.5 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



SECTION-2



Q.6 describe the following:[ Marks 8=2*4]


1) Lattice

2) Sub-Boolean algebra

3) Lattice homomorphism

4) Complemented lattices


b) define the list structure representation of a graph for storage with suitable example.[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


Q.9 a) describe the subsequent w.r.t groups:[Marks 8=2*4]

1. Order

2. Identity

3. Abelian

4. Degree

b) Let I be the set of integers. Prove that the algebraic system (I, +)is abelian group.[Marks 8]


Q.10.Write a short notes on:[Marks 18=6*3]

1. PERT

2. Generation of fault matrix

Earning:   Approval pending.