Shivaji University 2005 B.E Computer Science Discrete Mathematical Structure - exam paper
Sunday, 19 May 2013 11:15Web
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. |