B.C.A (Semester (CBCS) Examination Oct/Nov-2017
DISCRETE MATHEMATICS
Day Date: Saturday,18-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: All questions are compulsory.
Figures to the right indicate full marks.
Use of calculator is allowed.
Q.1 Choose the correct alternative. 14
The converse of the statement is
p→q

A relation is said to be equivalence if
Reflexive Transitive
Symmetric All of above
−

None of these
If is a prime no. from 1 to 20} then the cardinality of A is
8 9
10 20
Sets A B are said to be disjoint if
0
1 None of these
Which of the following is not a statement?
4 5 1
Mathematics is a difficult subject Mayuri is a beautiful girl
A Graph without any loop parallel edges is called
Simple Graph Multi Graph
Pseudo Graph Null Graph
If B are the subset of universal set then ′


If 1 object's are distributed into n boxes then at least one box contain's
object's.
One More than one
0 At least one
10) A Graph G having parallel edges but not loop is
Graph Multi Graph
Pseudo Graph Null Graph
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11) The cardinality of singleton set
1 2
0
12) A function is said to be Bijective if it is
One-one Onto
Both a b None of these
13) A compound statement which is Neither a tautology nor a contradiction is

Tautology Contradiction
Both Contingency
14) If a Graph G does not have any edge then the Graph is
Null Graph Simple Graph
Multi Graph None of the above
Q.2 Answers to the following. [Any seven] 14
Determine the No. of integer between 1 to 300 which are not divisible by 3.
Prepare the truth table for
If A 5 B then find A B and A B.
State the Inclusion Exclusion principle for three set B and C
Find the value of if the function
and 8.
If G be a given Graph.
Then Find G and G
Define symmetric difference of two set.
Find Adjancency Matrix for the following Graph.
If A and B then find A×B and B×A
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Q.3 Attempt any two of the following. 10
Test the validity of argument
p → q → r p
Let R be the Relation on the Set A given by R
Draw diagram of relation R. write also
find indegree and outdegree of elements of A.
Let U be a Universal set having Subset's A
B f }then find.

−
Define one-one function let f R→R be a function defined by

3

∈ Show that f is one -one.
04
Q.4 Attempt any two of the following.
How many integer between 1 to 567 which are divisible by either 3 or 5 or
Let R be a relation on set
A 4}. Find transitive closure of using Warshall's Algorithm. Also
draw diagraph of relation R*.
Prove that p → and → → are logically equivalent.
Q.5 Answer the following (Any 14
Define pseudo Graph and Find intersection and Ring sum of given two graph G1
and G2


State and prove Distribution property (both) for the sets, by using the universal
set
having subset
Define:
Complete Graph
Regular Graph
Power Set.
Surjective Function.