Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Year (First Year) Regulation-R19 2021 July-August 861AA Mathematical Foundations Of Computer Science Previous Question Paper
R19
Code No: 861AA
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
- - -
1.a)
Prove that the following statement is valid
p q
p (
q r)
s r
s
b) Find the conjunctive normal form of q ( p q
) ( p
q
) .
[7+8]
2.a)
Write the following sentences in the symbolic form
i) Arjun is a student
ii) All students like easy courses
iii) Sociology is an easy course.
b)
Prove that the following argument is valid.
No mathematicians are fools.,
No one who is not a fool is an administrator.
Sita is a Mathematician.
Sita is not an administrator.
[7+8]
3.a) Let A = (0, 1, 2, 3, 4) Show that the relation
R = [(0, 0), (0, 4), (1, 1), (1, 3), (2, 2), (3, 1), (3, 3), (4, 0), (4, 4)]
is an equivalence relation.
b)
Let X={1,2,3} and f, g, h and s be functions from X to X given by
f={(1,2), (2,3), (3,1)}, g={(1,2), (2,1), (3,3)} h={(1,1), (2,2), (3,1)}
Find: i) fog, ii) fohog.
[8+7]
4.a)
A={1,2,3,4}is a Relation R from A to A.
R={(1,1),(1,2),(2,3), (3,4),}. S = [ (3, 1), (4, 4),(2, 4), (1, 4)]
Determine
2
2
RoS, SoR, R , S .
b)
If f(x) = x+2, g(x) = x-2, h(x) = 3x, then find: i) gof ii) foh iii) hog .
[8+7]
5.a)
Using the principle of mathematical induction, prove that
n(n 1)(4n 1)
1 ? 2 + 3 ? 4 + 5 ? 6 + .... + (2n - 1) ? 2n =
3
b)
Prove that for any positive integer number n, prove that 3
n 2n is divisible by 3. [7+8]
6.a)
Use the mathematical induction to prove that
2
3n n for n a positive integer greater
than 2.
2021
b)
Using the principle of mathematical induction, prove that
1/(1 2) + 1/(2 3) + 1/(3 4) + ..... + 1/{n(n + 1)} = n/(n + 1)
[7+8]
7.a)
There are Three boxes I ,II and III Box I contains 4 Red 5 Blue and 6 White balls.
BoxII contains 3 Red 4 Blue and 5 White balls.
BoxIII contains 5Red 10 Blue and 5 White balls. One box is chosen and one ball is
drawn from it. What is the probability that
i) Red ball is chosen ii) Blue ball is chosen
iii) White ball is chosen
1
b)
Solve the recurrence relation. a
a 12a 10, a 0, a .
[7+8]
n2
n 1
n
0
1
3
8.a)
Prove that a graph G is a tree with n vertices if and only if It has (n-1) edges.
b)
Construct the minimum spanning tree for the following graph using Prim's algorithm.
[7+8]
16
V1 V2
19 21 11 5 6
18 V6 14 10 V3
V5 33 V4
---ooOoo---
This post was last modified on 16 March 2023