DISTANCE EDUCATION
M.Sc. (Computer Science) DEGREE EXAMINATION,
MAY 2017.
MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE
(2007 Onwards)
Time Three hours Maximum 100 marks
SECTION A — (10 3 30 marks)
Answer ALL questions.
1. Construct the truth table for .
2. Symbolize the statement
"All men are giants".
3. Define Power set. Give an example.
4. Let X and R 1,1 1,4 4,1
4,4 2,2 2,3 3,2 3,3 write the matrix
of R.
5. What do you mean by composition of functions?
6. Let f R R be given by f x3 2 . Find f .
7. Define the following Semigroup Monoid.
8. Find all the subgroups of Z12 .
9. Define Null graph Weighted graph.
10. What is a forest?
Sub. Code
11
DE-486
2
Sp 6
SECTION B — × 10 40 marks)
Answer any FOUR questions.
11. Show that P Q R.
12. Show that
.
13. What are the properties of Binary relations in a set? Give
examples.
14. Prove that for any commutative monoid the set
of idempotent elements of M forms a submonoid.
15. Let f x g x 2 and 3x for x R
where R is the set of real numbers. Find g f
f g f h h g .
16. Explain the matrix representation of Graphs with
examples.
SECTION C — × 15 30 marks)
Answer any TWO questions.
17. Obtain the principal conjunctive normal form and
principal disjunctive normal form of the formula
P .
18. Let R and S be two relations on a set of positive
integers I .
R x,2x I
S x,7x I
Find R S R R R and R R R .
19. State and prove Lagrange's theorem.