B.C.A (Semester (CBCS) Examination Nov/Dec-2018
DISCRETE MATHEMATICS
Time: 2½ Hours Max. Marks: 70
Instructions: All questions are compulsory.
Figures to the right indicate full marks.
Use of calculator is allowed.
Q.1 Choose and write a correct answer from given alternative. 14
The contrapositive form of the statement q → p is
p → q →
→ → p
If A is a prime number less than 28} then cardinality of set A is
9 27
28 10
If all the elements of matrix of relation R are 1 then relation R is relation.
void identity
reflexive universal
If every element of set A is related to unique element of set B then the relation R
defined from A to B is
function transitive
reflexive anti-symmetric
A B
A B − A B A − B − A B
A B A B A − B A B
The number of edges in K6 are
30 36
15 5
Which of the following is a statement?
10 4 10 for 8
is an even number − 2 0
The symmetric difference of the sets is
always commutative never commutative
symmetric none of these
The relation R which is reflexive, and transitive is called as partial
ordering relation.
symmetric anti-symmetric
equivalence asymmetric
10) Multiplication principle is
× A . B A B A B
A B A B − A B A B A B
11) If G1(V1, E1) and G2(V2, E2) be the two graphs then vertex set of the graph
G G1 ⊕ G2 is
V1 ⊕ V2 V1 V2
V1 V2 V1 × V2
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12) If is true statement and is false statement then the truth value of the
statement → is
T F
both none of these
13) If − 5 then is
15 11
1 0
14) A null graph N5 is regular graph.
4 5
0 10
Q.2 Answer the following (Any Four) 08
State distributive Laws of sets.
If are true statements and are false statement, the find the
truth value of the compound statement
→ → ↔ ↔
Define symmetric relation.
Define domain and co-domain of a function.
State principle of mutual inclusion-exclusion for two sets. Hence find
A B where A 35, B 20, and A B 15
Q.2 Answer the following (Any two) 06
Define complete Graph. Hence draw the graph K4
Define disjoint sets. Give example.
Let A r B d}. Find A × B and B × A. Is Cartesian product
commutative?
Q.3 Attempt any two of the following. 08
State and prove any one Demorgan's Law in logic.
Write adjacency and incidence matrix for the following graph.
G
Let R be the relation defined on the set A given by R
b a d b d a d b a Write matrix of
relation R. Also draw digraph of relation R.
Q.3 Answer the following. (Any One) 06
From the following graphs, draw the graphs G1 G2 and G1 ⊕ G2
V1
V2
V3
V4 V5
e1
e2
e3
e4 e5
e6
e7
e8
e9
e10
V1
V2 V3
V5 V4
G1
G2
V2
V3
V4 V5
V6 V7
a
b
c
d
e
e1
e2
e3
e4
e5
e7
e8
e9
e2
e3
e7
e9
e6
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How many integers between 1 to 2002, which are divisible either by 2
or by Also find how many integers are not divisible neither by 2 nor
by
Q.4 Answer the following: (Any Two) 10
Define injective function, surjective function and bijective function.
Let U 10} the universal set. Let A 10
B 10} be the subsets of U. Write the sets
A′ A A − A ⊕ B − A
p q q ↔ q → p
Determine whether the following statement is tautology or contradiction
or neither.
Q.4 Answer the following (Any one) 04
From the following graph draw the graphs,
i. G − V1
ii. G − V3}
iii. G − e4
iv. G − e3, e5, e2}
G
Define equivalence relation and universal relation.
Q.5 Answer the following. (Any 14
Define cardinality of a set. Hence write the following sets find their
cardinalities.
A − A B ⊕ B′ B C. Where U is universal
set. A B C
Test the validity of the following argument.
p r p ↔ r p q
State and prove principle of mutual inclusion-exclusion for three sets.