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Posted Date: 02 Jan 2008 Posted By: Girish Patil Member Level: Platinum
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2006 Shivaji University B.E Computer Science DISCRETE MATHEMATICAL STRUCTURE Question paper
Y-308
SECOND YEAR OF COMPUTER SCIENCE AND ENGINEERING (PART-1) EXAMINATION, 2006
SHIVAJI UNIVERSITY, KOLHAPUR
DISCRETE MATHEMATICAL STRUCTURE
Day and Date: Wednesday, 30-11-2006 Total Marks: 100
Time: 3.00p.m. To 6.00p.m.
Instructions: 1) Attempt any three questions from each section.
2) Figures to right indicate full marks.
SECTION-1
Q.1 a) shows the following 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 following 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? Define the following 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) Define the lattices as a POSET. Define greatest lower bound and least upper bound with examples.[Marks 8]
b) Define group. Define and give examples of different types of groups.[Marks 10]
Q.6 a) Explain about the recovery of single error in group codes.[Marks 8]
b) Explain the linked representation of binary tree.[Marks 8]
Q.7 a) Explain the inorder traversal algorithm for the tree structure. [Marks 8]
b) For the Boolean function F=XYZ+XYZ+XYZ give the following 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 following expressions: :[ Marks 8=4*2]
1) a + (b/c) *d
2) (a + b) (c + d/e) * f
b) What is diagraph? Define the following:[Marks 8]
1. asymmetric diagraph
2. converse of a diagraph
3. reflexive diagraph
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