DISTANCE EDUCATION
B.Sc. (Computer Science) DEGREE EXAMINATION,
MAY 2016.
DISCRETE MATHEMATICS
(2007 onwards)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
All questions carry equal marks.
20 100)
1. Construct truth table for P .
Prove P
Explain about conditional and bi-conditional
statements.
Symbolize the expression "All the world loves a
lover". 5 5
2. What are set operations? Explain with examples.
Show that for any two sets A and B
A A B . (10 10)
3. Let X and
R y y is divisible by
Show that R is an equivalence relation.
Let R and S be two relations on a set of positive
integers I.

S x x x
R x x x I



2
Find R and . (10 10)
Sub. Code
15
DE-3397
2
ws 8
4. Write all possible functions from x to
y and classify them into one-to-one onto,
neither one-to-one nor onto types of functions.
If f and are bijections, prove that
g f is also a bijections. (10 10)
5. What do you mean algorithm? Explain the
complexity of algorithms.
Define and give examples for the following
Semi group
Monoid. (10 10)
6. State and prove Lagrange's theorem.
If is an abelian group, then for all .
Show that an . (10 10)
7. Find the left cosets of in the group
z6 t6 .
Define the following with examples.
Complete graph
Bipartite graph
Regular graph
Null graph. (10 10)
8. Define Adjacency matrix of the graph and find the
adjacency matrix of the following graph.
Explain the Konigsberg bridge problem. (10 10)