Vinayaka Missions University 2010 Post Graduate Diploma Computer Application Mathematical foundation of computer science - Question Paper

COURSE CODE - 3050110
PG DIPLOMA exam – JAN 2010
PGDCA
MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE
(For Candidate Admitted from Calendar 2007 Onwards)
Time: three Hours Max.Marks:75
PART-A
ans all the Questions: 10 X two = 20
1. How many various words are there in the word Mathematics?
2. What is Combination?
3. What is ring?
4. ~ (PnQ) ??
5. describe Hass diagram
6. describe Conditional statements
7. describe Po-set.
8. describe Total Function.
9. describe the truth value of a statement?
10. describe Primitive recursive function.
PART-B
ans all the Questions: five X five = 25
11. a. discuss about Homomorphism
(Or)
b. Is the posit (z+, /) a lattice? And Let S = {a, b, c}. Draw the diagram
of (P(s), ? ).
12. a. In a group the right and left cancellation laws are actual. ie a*b =
a*c ? b=c.& b*a = c*a ?b=c
(Or)
b. discuss about primitive functions.
13. a elaborate the rules of Inference?
(Or)
b. (i) for any group G, if a2 = e with a ? e then G is abelian.
(ii) Prove (a*b)-1 = b-1* a-1
14. a. Show that f (x,y) = xy is a primitive recursive Function
(Or)
b. Write short notes on Book algebra
15. a. discuss about normal subgroups
(Or)
b. Show that in any Boolean algebra (a + b) (a1+c) = ac +a1b +bc
PART- C
ans any 2 Questions: two X 15 =30
16. Show that (?x)(H(x) ? M(x)) ? H( y) ? M( y)
(ii) Show that (?x)(P(x) ? Q(x)) ? (?x)P(x) ? (?x)Q(x)
17. Briefly discuss partially order set
18. obtain the principle disjunctive normal form and principle conjunctive
normal form of the formula
PU (7p?(QV(Q ?)))
19. Solve the recurrence relation f(n) – 8f (n-1) + 16f (n-2) = 0;
n = 2, Where f (2) = 16, f (3) = 80.
20. Show that every finite integral domain is field.

Earning:   Approval pending.