Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R15 2021 July-August 821AA Mathematical Foundations Of Computer Science Previous Question Paper
R15
Code No: 821AA
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
2021 MCA I Semester Examinations, July/August - 2021
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Time: 3 Hours
Max.Marks:75
Answer any five questions
All questions carry equal marks
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1.a)
Prove by indirect method that (? Q), P Q, P R R
b)
What are the most common rules of inference?
[7+8]
2.
Write in the symbolic form and negate the following statements:
a) Everyone who is rich can support charity.
b) Some people are not appreciated by everyone.
c) Everyone should help their friends, or their friends will not help them.
[5+5+5]
3.a)
Show that the relation of congruence modulo m has `m' distinct equivalence
classes.
b)
Let C be a collection of sets which are closed under intersection and union. Verify
whether (C, , ) is a lattice.
[7+8]
4.a)
Define monoid. Give examples.
b)
State the laws of Boolean algebra.
[7+8]
5.a)
How many words of length six over the alphabet {a, b, c, d, e} contain two a's, three b's
and two c's.
b)
Find the number of ways the letters of the word MALAYALAM can be scrambled. [7+8]
6.
State and explain pigeon-hole principle and explain its applications in detail.
[15]
7.
Solve the recurrence relation un+2 -5un+1+6 un=n .
[15]
8.
What is a spanning tree? What is minimum spanning tree? Explain Prim's algorithm for
finding it with illustration.
[15]
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This post was last modified on 16 March 2023