Download JNTUA MCA 2018 July Reg-Supply 1st Sem 9F00104 Mathematical Foundations of Computer Science Question Paper

Download JNTU Anantapur (JNTU Anantapur) Master of Computer Applications (MCA) 2018 June-July Regular Supply 1st Sem 9F00104 Mathematical Foundations of Computer Science Previous Question Paper

Code: 9F00104

MCA I Semester Supplementary Examinations June/July 2018
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
(For 2011 (LC), 2012, 2013, 2014, 2015 & 2016 admitted batches only)

Time: 3 hours Max. Marks: 60

Answer any FIVE questions
All questions carry equal marks
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1 (a) Verify the identity, inverse and domination laws through truth tables.
(b) Show that using (i) truth table. (ii) without truth table.

2 (a) Test whether the following argument is valid
I will get grade A in this course or I will not graduate.
If I do not graduate, I will join the army.
- - - - - - - - - - - - - - - - - - - - - - - - - - -
Therefore, I will not join the army.
(b) Prove the statement ?The square of an even integer is an even integer? by the method of
contradiction.

3 (a) Explain about the properties of a binary relation in a set with suitable example.
(b) Define a partial order relation. Let A be a given finite set and P (A) its power set. Let be the
inclusion relation on the elements of P (A). Draw Hasse diagrams of


4 (a) Write about general properties of an algebraic system.
(b) With an example, explain the concept of homomorphism and isomorphism.

5 (a) Find the coefficient of x
9
y
3
in the expansion of (2x-3y)
12
.
(b) Explain the principle of inclusion-exclusion with a suitable example.

6 Find a generating function for the recurrence relation a
n+2
- 5a
n+1
+6a
n
= 2, n ? 0 and a
0
= 3, a
1
= 7.

7 (a) Prove that the sum of degrees of the regions of a planar graph G is equal to twice the number of
edges in G.
(b) What is a spanning tree? Explain any two ways for finding out spanning tree of a given graph with
examples.

8 (a) Find the chromatic number of:
(i) A bipartite graph . (ii) A complete graph .
(b) What is a Euler circuit? Explain the process of finding a Euler circuit in a given graph.

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