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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA Integrated SEMESTER- 1 EXAMINATION WINTER 2018
Subject Code: 2618604 Date: 08-01-2019
Subject Name: Basic Mathematics for IT
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:
Null set
Union of two sets
Symmetric Matrix
Universal Quantifiers
Reflexive Relation
Mixed Graph
Isolated vertex
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Let U

XΔY, using Venn Diagram. (Note: XΔY

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Q.2 Check whether the statements are tautology or not.(using truth table)
→
ii)
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Each student in a class of 40 plays at least one indoor game chess, carrom and scrabble.
18 play chess, 20 play scrabble and 27 play carrom. 7 play chess and scrabble, 12 play
scrabble and carrom and 4 play chess, carrom and scrabble. Find the number of students
who play chess and carrom. chess, carrom but not scrabble.
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OR
Using Predicate, Quantifier and rule of inference determine the given argument is valid or not
"All student in the class understand logic. Xavier is a student in this class. Therefore, Xavier
understand logic."
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Q.3 For an integer x prove that the following statements are equivalent:
x is divisible by 10.
x is divisible by 2 and 5.
x is an even number and x is divisible by 5.
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If
1 2 3
4 2 5
A



and
2 3
4 5
2 1
B





then find AB, BA. Show that AB BA
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OR
Q.3 Let X Draw a graph of R and also give its matrix. Check
whether the given relation an equivalence relation?
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2
3 3 3 3
1 2 3 .........
2
n n
n



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Q.4 Define Composition of a function. Let and f,g,hand s be functions from X to X
given by f g
h s
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2
Find fog fohog, sog, gos, sos.
Name different techniques of proof. Explain "the method of proof by contradiction", giving
suitable example.
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OR
Q.4 Explain basic properties of integer with examples. 07
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 .
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Q.5 Define node base of a diagraph. Find all node base of the digraph given below
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Define adjacency matrix of a graph and obtain the adjacency matrix for the following
graph. Find AT. Also draw graph of AT and find Path matrix P.
07
OR
Q.5 Define Binary tree. Convert the given tree into the Binary tree

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Define: Isomorphic Graph. Verify the following graphs are isomorphic or not.(Justify)
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