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

__MODEL EXAMINATION__

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__DISCRETE MATHEMATICS__

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**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.**

Earning: Approval pending. |