MCA-09
June Examination 2016
MCA IInd Year Examination
Discrete Mathematics
Paper MCA-09
Time 3 Hours Max. Marks 80
Note: The question paper is divided into three sections B and C. Use of non-programmable scientific calculator is allowed in this paper.
Section A 8 × 2 16
(Very Short Answer Questions)
Note: Section contain Very Short Answer Type questions each question is of 02 marks. Examinees will have to answer all questions.
Express the set A x x is letter in word CAT} in Roster form.
Define a function from set A to B.
Define a statement.
Define Tautology.
515
MCA-09 200 4 (P.T.O.)
515
MCA-09 200 4 (Contd.)
Prove that is logically valid.
Explain binary operation.
State De-Morgen's law for Boolean algebra.
(viii) How many numbers between 1 to 200 are divisible by 4.
Section B 4 × 8 32
(Short Answer Questions)
Note: Section contain Short Answer Type Questions.
Examinees have to answer any four questions. Each
question is of 08 marks.
Prove that:
A AkB
AjB= and
If X be the set of real number excluding 1. Show that the
function f x x
x
1
1 "
is one-one and on to.
Explain the following logical connection
Negation
Conjunction
Disjunction
Conditional
Using truth table prove that
0 is a contradiction.
MCA-09 200 4 (P.T.O.)
515
If D 8
be the set of all divisors of 8 and let and
be two operations defined on D8 as follows:
a b a b
a b a b
LCM of and
GCD of and


also for each a a a
D 8 8
1 then prove that D 8 i is not
a Boolean algebra.
How many 3 letters words can be formed?
With out repetition
Repetition of letters is allowed
In how many ways can 5 gents and 4 ladies dine at a round table
if no two ladies are to sit together.
Examine If the ring
R bi b are integers, i 1 is a field also check
for integral domain.
Section C 2 × 16 32
(Long Answer Questions)
Note: Section contain 04 Long Answer Type Questions.
Examinees will have to answer any two questions.
Each question is of 16 marks.
10) Prove that the number of vertices of odd degree in a graph
is always even.
515
MCA-09 200 4
Show that the simple graphs with following adjacency
matrices are isomorphic.
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
R
T
SSSS
R
T
SSSS
V
X
WWWW
V
X
WWWW
11) Prove that in any tree with two or more vertices there are
at least two pendant vertices.
Prove that every non-zero finite integral domain is a field.
12) Prove that every finite group of order less than or equal to
five is commucative group.
Prove that every quotient group of a cyclic group is cyclic.
13) Prove that any two left (right) cosets of a subgroup are
either disjoint or identical.
State pigen hole principle. Use pigen hole principle to
find among 100 people. How many people born in same
month.