M.C.A. (Semester (CBCS) Examination Oct/Nov-2017
Science
DISCRETE MATHEMATICAL STRUCTURES
Day Date: Tuesday, 21-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Questions No.1 and 2 are Compulsory.
Attempt any three questions from Q.No.3 to Q.No.7
Figures to the right indicate full marks.
Q.1 Choose the correct alternative given in the bracket. 10
There is no more than one edge between a pair of vertices is called.
Multi graph Regular graph
Simple graph None of these
2 A relation R on a set A is called Poset if.
Reflexive Anti symmetric
Transitive All of the above
3 In how many ways committe of 6 be chosen from 10 people.
P C
P C
4 In a group G which of law is called commutative.
a b b a a e e a a
a a-1 a a None of these
5 The main function of logic is to provide which of the following.
Valid argument Valid conclusion
Rules of inference None of these
6 Which is the technique of defining of itself a set or an algorithm in term
of itself
Recursion Regression
I Inference None of these
7 Any arrangement of a set of objects in given order is called.
Combination Permutation
Partition None of these
8 A single vertex with single loop is cycle of length is.
Zero One
Two Three
9 The Inverse of any matrix A is.
One Unique
Different Equal
1 In the set theory
U
U
Page 2 of 2
SLR-SM-3
Fill in the blanks 04
If A B are two matrices of same order then
The proposition that are assume to be true are called
It is defined as smallest transitive relation containing R.
A lattice is called bounded lattice if
Q.2 Compute P P 04
Show that npn-1
1 04
Define function with example 03
Check the validity of the following arguments.
All men are mortal. Socrates is a man therefore Socrates is mortal.
03
Q3 Explain Hasse diagram. Draw Hass diagram D20 07
A family of 3 sisters 5 brothers to be arrange for a photograph. In how many
ways they can be sited if.
No condition
All the sister sit together
07
Q4 Let G be the set of all non zero real number a*b
ab
2
show that is group. 07
Let X Y Z R Let X → Y
g Y → Z are such that f 1
g y
y
3
verify (gof)−1 f −1og−1
07
Q.5 Explain Regular graph planner graph with example. 07
Prove that the following equivalence P Q → ≡ Q 07
Q.6
x − y z 4
2x y − 3z 0
x y z 2
Solve the following equation by inversion method. 07
Define an equivalence relation. If R is a relation define the "squre"
Let S IR, R x2 y2}
Prove that squre relation is an equivalence relation.
07
Q.7
H
0 1 1
0 1 1
1 0 0
0 1 0
0 0 1
For the parity check matrix.
Determine encoding fun eH B2 → B5
07
Show that SVR is tautologically implied by → → 07