Posted Date: 19 May 2013      Posted By:: Jp    Member Level: Gold  Points: 5 (₹ 2)

2010 Shivaji University General B.E DiscRETE MATHEMATICAL STRUCTURE Question paper

 Course: B.E University/board: Shivaji University

Are you searching for the old question papers of Shivaji University? I have uploaded the Shivaji University previous year question paper from Shivaji University. This is the original question paper from the B.E exam conducted by Shivaji University year 2010. It is for your use and so download the question paper from here and prepare for your upcoming exams well.

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

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