Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Sem (First Semester) Regulation-R17 2018 June-July 841AA Mathematical Foundations Of Computer Science Previous Question Paper
R17
Code No: 841AA
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, June/July - 2018
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Time: 3hrs
Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A
5 ? 5 Marks = 25
1.a) Construct the truth table for (P Q) (P Q) .
[5]
b) Define complement of a function and inverse of a function. Give examples.
[5]
c) Find the coefficient of x4y7 in the expansion of (x-y)11.
[5]
d) What is meant by generating function? What is its significance?
[5]
e) Find the minimum number of vertices in a simple, connected, planar graph with 19 edges.
Justify your answer.
[5]
PART - B
5 ? 10 Marks = 50
2.a)
Using indirect method of proof, derive P ? S from P Q R, Q ? P, S ? R, P.
b)
Contrast propositional logic with predicate logic.
[5+5]
OR
3.
Explain automatic theorem proving with the following expression
P, ? P ( P Q) Q
[10]
4.a)
If f : XY and g : YX the function g is equal to f-1 only if g ? f = Ix and
f ?g = Iy .Prove the result.
b)
Let f : R R and g : RR where R is the set of real numbers. Find f ?g and g ? f where
f(x) = x2 - 2, g(x) = x + 4. State whether these functions are injective, subjective or
objective.
[5+5]
OR
5.a)
Let L a finite distributive lattice. Then prove that every element in L can be written
uniquely (except for order) as the join of irredundant join-irreducible elements.
b) Prove the independent laws for the elements of a lattice.
[5+5]
6.
Find the number of ways three roses, four marigolds and five hibiscuses can be planted:
a) In a row such that all plants of the same family is next to each other.
b) In a row such that the hibiscus are planted in between the other two families of plants.
[5+5]
OR
7.a)
Find the number of different arrangements of the letters of the word REFERENCE.
b)
State inclusion-exclusion principle.
[5+5]
8.
Solve the recurrence relation an-7an-1+26an-2 - 24an-3=0 for n>= 2.
[10]
OR
9.
Demonstrate the solutions for non-homogeneous recurrence relation.
[10]
10.a) Prove that any two simple connected graphs with n vertices and all of degree two are
isomorphic.
b) Suppose G1 and G2 are isomorphic prove that if G1 is connected then G2 is
also connected.
[5+5]
OR
11.a) State and explain the Four - Colour problem for planar graphs.
b) Prove that the regions of a planar graph can be 4 - coloured if G has a Hamiltonian cycle.
[5+5]
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This post was last modified on 16 March 2023