Anna University Coimbatore 2009 B.E Computer Science and Engineering Discrete Mathematics Model - Question Paper

MODEL EXAMINATION

 

DISCRETE MATHEMATICS

 

Year/Branch/Sem : II /IT , CSE / IV Marks: 100

PART-A (20 X 2 = 40)

1.    Obtain PDNF for .

2.    Give the converse and the Contra positve of the implication If it is raining then I get wet.

3.    Represent using only.

4.    Determine the truth value of the following a) If 3+4=12 , then 3+2=6.

b) If 3+3=6 , then 3+4=9.

5. State Simple statement function.
6. Express the statement For every x there exist a y such that in symbolic form.
7. Give the symbolic form of the statement

Every book with a blue cover is a Mathematics book.

8. Symbolize the expression (i) All the world loves a lover
9. For any sets A , B and C , Prove that .
10. Give an example of a lattice which is modular but not distributive.
11. Give an example of a relation which is symmetric but not reflexive
12. Define Characteristic function.
13. If denotes the characteristic function of the set .Prove that

for all .

14. If has 3 elements and has 2 elements. How many functions are there from to .
15. Define odd and even permutation.
16. Show that is a binary operation on the set of positive integers.
17. Let and where is the set of real numbers. Find where .
18. A semi group homomorphism preserves property of associativity
19. Find all the cosets of the subgroup in with the operation multiplication.
20. Define abelian group and subgroup.

 

PART-B (Answer any 5) (5 X 12 =60 )

 

21. a)Find the PDNF and PCNF of the formula

.

 

 

 

 

b) Show that the following premises are inconsistent:

1. If Jack misses many classes through illness and reads a lot of

books.

2. If Jack fails high school, then he is uneducated.

3. If Jack reads a lot of books, then he is not uneducated.

4. Jack misses many classes through illness & reads a lot of

book

22. a)Using Indirect method of proof , derive from

b) Prove that .

23. a)Show that b)Prove that any chain a is modular lattice.
24. a) Show that if L is a distributive lattice then for all

.

b)Let R denote a relation on the set of ordered pairs of positive

integers such that iff . Show that R is an

equivalence relation.

25. a)If & are permutations,

prove that .

b) Let the function and be defined and

.Determine the composition function and

.

26. a) Show that .

b) Show that encoding function defined by

is a

group code.

27. State and prove Fundamental theorem on Homomorphism of groups.
28. a) If is the parity check-matrix. Find the Hamming code generated by .If is the received word ,find the corresponding transmitted code word.

b)Find the minimum distance of the encoding function given by .