Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Year (First Year) Regulation-R19 2020 November 861AA Mathematical Foundations Of Computer Science Previous Question Paper
S OCT 2020
R19
Code No: 861AA
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, October/ November - 2020
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Time: 2 Hours
Max.Marks:75
Answer any five questions
All questions carry equal marks
- - -
1.a)
Show that (pq) (pq) is a tautology using logical equivalences and truth table.
b)
Let p and q be the propositions.
p :You drive over 65 miles per hour.
q :You get a speeding ticket.
Write these propositions using p and q and logical connectives (including negations).
used
i) You do not drive over 65 miles per hour.
ii) You drive over 65 miles per hour, but you do not get a speeding ticket.
iii) You will get a speeding ticket if you drive over 65 miles per hour.
iv) If you do not drive over 65 miles per hour, then you will not get a speeding ticket.
v) Driving over 65 miles per hour is sufficient for getting a speeding ticket.
[7+8]
2.a)
Let p and q be the propositions.
p :I bought a lottery ticket this week.
q :I won the million dollar jackpot.
Express each of these propositions as an English sentence.
i) pq
ii) p q
iii) p q
iv) ? p ? q v) ? p? q
b) Show that the premises "A student in this class has not read the book" and "Everyone in
this class passed the first exam" imply the conclusion "Someone who passed the first
exam has not read the book".
[7+8]
3.a)
Let A ={0,2,4,6,8}, B ={0,1,2,3,4}, and C ={0,3,6,9}. What are (A B C) and
(A B C)?
b)
Draw the Venn diagrams for each of these combinations of the sets A, B, and C.
i) A (B -C)
ii) (AB) (AC)
c)
Define one-to-one and on-to functions.
[6+6+3]
4.a)
Find fog and gof, where f(x)= 2x +1 and g(x)= x2 + 1, are functions from R to R.
b)
How can we produce the terms of a sequence if the first 10 terms are 5, 11, 17, 23, 29, 35,
41, 47, 53, 59?
c)
Let R = { (a,b), (b,c), (c,d), (d,e), (c,a), (a,c), (e,b)} be a relation on the
set A = {a,b,c,d,e}. Find the transitive closure of the relation R.
[5+5+5]
S OCT 2020
5.a)
Determine whether each of the functions 2n+1 and 22n is O(2n).
b)
Give a recursive algorithm for computing the greatest common divisor of two non-
negative integers a and b with a < b.
[7+8]
6.a)
Find the probability that a hand of five cards in poker contains four cards of one kind.
b)
What is the probability that a positive integer selected at random from the set of positive
integers not exceeding 100 is divisible by either 2 or 5?
c)
Define conditional probability.
[6+6+3]
7.a)
Find the solution to the recurrence relation: an = 6an-1 -11an-2 +6an-3 with the initial
conditions a0 = 2, a1 = 5, and a2 = 15.
b)
Use generating functions to find the number of k-combinations of a set with n elements.
Assume that the binomial theorem has already been established.
[7+8]
8.
Devise the algorithms for DFS and BFS and explain the differences between them with
an illustrative example.
[15]
used
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This post was last modified on 16 March 2023