Vinayaka Missions University 2008 Post Graduate Diploma Computer Application MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE : t : Correspondence - Question Paper

COURSE CODE – 3050110
PG DIPLOMA exam – SEP 2008
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:- 15 X 1=15
1. Write down the truth table for negation.
2. State conjunction.
3. State predicate calculus.
4. ~ (PnQ) ? ?
5. describe permutation.
6. describe combination.
7. State pigeonhole principle.
8. describe semi group.
9. describe mooned.
10. describe subgroup
11. describe Ring.
12. describe lattices.
13. describe partial ordering.
14. describe Boolean algebra.
15. describe Modular.
part - B
ans any 5 questions:- five X six = 30
16. a. elaborate the rules of Inference.
(Or)
b) find disjunctive normal forms of
(i) Pn(P?Q)
(ii) seven ( PUQ) ?????? (PnQ)
17. a) Prove that if n pigeons all assigned to m pigeonholes the
one of the pigeonholes must contain attest L(n-1) /m +1
pigeons.
(Or)
b) Write about principle of inclusion & exclusion.
18. a) (i) For any group G, if a2 = e with a ? e then G is abelian.
(ii) Prove (a*b)-1 = b-1* a-1
(Or)
b) In a group the right and left cancellation laws are actual. ie
a*b = a*c? b=c.& b*a = c*a? b=c
19. a.) State and prove properties of lattios.
(Or)
b) Show that in any Boolean Algebra
(a+b) (a1+c) = ac +a1b +bc
20. a) Write about recursive functions.
(Or)
b) discuss in detail primitive functions.
part – C
ans any 2 questions:- two X 15 = 30
21. obtain the principle disjunctive normal form and principle
conjunctive normal form of the formula
PU (7p?(QV(Q ?)))
22. discuss permutation & combination with example
23. State and prove lagranges theorem
24. (a) Prove every finite Boolean Algebra is atomic.
(b) If ( , ? ,n) be complemented distributive laltice then for
any a, b,? . Prove
(i) a ? b =a nb
(ii)anb =a ? b
25. Briefly discuss computable functions.

Earning:   Approval pending.