Anna University Coimbatore 2008 B.E Computer Science and Engineering Discrete Mathematics Model - Question Paper
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.
Earning: Approval pending. |