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# Anna University Coimbatore 2008 B.E Computer Science and Engineering Discrete Mathematics Model - Question Paper

Wednesday, 16 January 2013 07:05Web

MODEL EXAMINATION

MODEL EXAMINATION

DISCRETE MATHEMATICS

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

Time:9.10-12.10

PART-A (20 X 2 = 40)

1.    Write the dual of (a) (b) (c) .

2.    Show that .

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.    Find the truth value of where .

6.    Prove that .

7.    If the universe of discourse is the set eliminate the quantifiers in the formula .

8.    Give the symbolic form of the statement

Every book with a blue cover is a Mathematics book.

9.    For any sets A , B and C , Prove that .

10. Define Characteristic function.

11. Define Partially ordered set.

12. Give an example of a relation which is both reflexive and

symmetric.

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. Define Partially ordered set.

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 ring and give an example of a ring with zero-divisors.

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

21. Without using truth tables & also use truth tables,Obtain PDNF

& PCNF of .

22. a) 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

b) Using Indirect method of proof , show that 23. a) Prove that .

b) Show that 24. a)Show that if L is a distributive lattice then for all  .

b)Establish De Morgans laws in a Boolean algebra.

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

integers such that iff . Show that R is an

equivalence relation.

b)Prove that any chain a is modular lattice.

26. a)If & are

permutations, prove that .

b) Let the function and be defined and .Determine the composition function and .

27. a). Find all the mappings from to find

which of them are and which are onto.

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

28. a)State & prove Lagranges theorem for finite groups.

b) Show that encoding function defined by is

a group code. 