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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- III EXAMINATION WINTER 2018
Subject Code: 4639301 Date: 02-01-2019
Subject Name: Basic Mathematics
Time: 10.30 am to 1.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Give definition of the following terms:
Singleton set
Intersection of two sets
Transpose of a Matrix
Existential Quantifiers
Symmetric Relation
Complete Graph
Pendent vertex
07
For A B C find

If
Find X U X
X X
07
Q.2 p prepare the truth table. 07
Test the validity of the logical consequences:
All dogs fetch.
Ketty does not fetch.
Therefore, Ketty is not a dog
07
OR
In a competition, a school awarded medals in different categories. 36 medals in
dance, 12 medals in dramatics and 18 medals in music. If these medals went to
a total of 45 persons and only 4 persons got medals in all the three categories,
how many received medals in exactly two of these categories?
07
Q.3 Explain contradiction method and using it prove that 6 is an irrational
number.
07
Compute, AT,BT,AB

0 0 1
1 0 1
0 1 1




and B
1 0 1
1 1 0
0 0 1




07
OR
Q.3 Let X x is divisible by y}. Draw a graph of R and also
give its matrix. Check whether the given relation an equivalence relation?
07
1 1 1 1 1
.......... 1
2 4 8 2 2 n n
07
Q.4 Let f R and g Rwhere R is the set of real numbers. Find fog and
gof where 2 f x x 4 State whether these functions are
injective, surjective, and bijective.
07
2
Let X and be the relation as follows:
Write properties of R .
Write matrix of R .(iii) Find S oT, R o S and S o R .
07
OR
Q.4 Define Tautology and Contradiction with examples. Prove that is
tautology without constructing truth table.
07
List all possible functions from X indicate in each case
whether the function is one-to-one is onto, and is one-to-one onto.
07
Q.5 Define Strong, unilateral week component. Also Find Strong, unilateral, week
component from the given digraph.
07
Define adjacency matrix of a graph and obtain the adjacency matrix for the
following graph. State the in degree and out degree of all the vertices. Find A2, B2
and Path matrix P.
07
OR
Q.5 Define Tree.
Give three different representation of the given tree.

07
Define: Isomorphic Graph. State whether the following graphs are isomorphic
or not:
07