DISTANCE EDUCATION
M.C.A./M.C.A. (Lateral) DEGREE EXAMINATION,
MAY 2017.
Third Semester
DISCRETE MATHEMATICS
(2005 to 2010 Calendar year)
Time Three hours Maximum 100 marks
Answer any FIVE questions.
All questions carry equal marks.
× 20 100)
1. Show that
P Q R Q R P R
Obtain the principal disjunction normal form of
P
2. Show that is a valid conclusion from the
premises P and M .
Show that
.
3. What are the operations performed on set? Explain
with examples.
If A and B what are
and
Sub. Code
31
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4. What do you mean by an equivalence relation?
Explain with example.
Let R and S be two relations on a set of positive
integers I .
R x,2x x
S x,7x x
Find R R R R and R S
5. What are the types of function? Explain with
examples.
Let f and R where R is the set of
real numbers. Find f g and g f where
f 2 and x 4 . State whether these
functions are injective, surjective and bijective.
6. What are the general properties of algebraic
system? Explain.
Show that the set N of natural numbers is a
semigroup under the operation x y max . Is
it a monoid.
7. State and prove Lagrange's theorem.
Define the following with examples
Undirected graph.
Subgraph.
Simple graph.
Degree of the graph.
Path of the graph.
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8. Write the Warshall algorithm to find the path
matrix of the graph and give one example.
Define any five terminologies related to trees with
examples.