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Posted By: satish Member Level: Gold Posted Date: 10 Feb 2008
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2005 Jawaharlal Nehru Technological University II B.Tech I Semester Supplementary Examinations, November 2006 set 1 Question paper
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Code No: RR210501 Set No. 1
II B.Tech I Semester Supplementary Examinations, November 2006
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Common to Computer Science & Engineering, Information Technology,
Computer Science & Systems Engineering and Electronics & Computer
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Show that RVS follows logically from premises. [8+8]
C D, (C D)® !? H,? H ®(A ^ B) (A ^ B) ® R S
(b) Show that R® S can be derived from the premises P® (Q® S), ? R P and
Q.
2. (a) What are the properties of the relation r = ( i, j ) / |i j|
= 2 on the set
A = { 1, 2, 3, 4, 5, 6 }. [8+8]
(b) Determine all the bijections from { 1, 2, 3 } on to {a, b, c, d}.
3. (a) Show that for any fixed k the relation given by {< k, y > |y > k} is primitive
recursive. [8+8]
(b) Show that the sets of even numbers and odd numbers are both recursive.
4. (a) Are the graphs shown in the figure1 isomorphic ? [8+8]
Figure 1
(b) Define isomorphism and give examples.
5. (a) Prove that the Kuratowskis second graph consisting of 6 vertices and 9 edges
is nonplanar.
(b) State criteria to detect the planarity of a connected graph and give an example
also.
[8+8]
1 of 2
6. (a) Do an analysis of the DijkstraPrim
minimum spanning tree algorithm, counting
the number of times that an edge is considered for nodes added to the
fringe, for updating edges to the fringenodes, or to pick the node to move
from the fringe to the minimum spanning tree. [10]
(b) What is the value of the postfix expression. [6]
723 * 4
? 93 / + ?
Give the solution steps.
7. (a) Explain the terms [10]
i. Disjunctive counting and
ii. Sequential counting.
(b) How many numbers can be formed using the digits 1, 3, 4, 5, 6, 8, and 9 if no
repetitions are allowed? [6]
8. Solve the recurrence relation. an7a
n-1+
26 an-2 - 24an-3=0 for n= 2.
[16]
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