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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- III EXAMINATION WINTER 2018
Subject Code: 3630001 Date: 04-01-2019
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

Define the following
Intersection of two sets
Transpose of a matrix
Power Set
Modus pones
Posets
Binary Tree
07

Let U
A
B
C
Compute, AΔB, using Venn
Diagram. (Note: AΔB
07
Q.2

Show the following implication without constructing truth table and thereafter show it through the truth tables
P V
07

Express the following using predicates, quantifiers and logical connectives.
Also verify the validity of consequence
All birds can fly
A sparrow is a bird
Therefore, a sparrow can fly.
Prove by contradiction that an irrational number
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04
OR

Define Relation . Let and R x>y }.Draw the graph of R and also give its matrix.
07
Q.3

What is Recursive Function? Write a Recursive algorithm to find out Fibonacci series.
07

Draw the Hasse diagrams of the following sets under the partial ordering relation "divides" and indicate those which are totally ordered.

07
OR
Q.3

Let and the relation be such that x≤y if x divides y. draw
the Hasse Diagram of
07

Let bed, dog, let, egg} and let the relation R be given as: x,y
if x and y contain some common letters.}
Identify a relation. Draw a graph for R and find maximal compatibility block for
the same.
07
2
Q.4

Explain with example injective surjective(one-to-one) and bijective(one-to-one onto) function. Let N be set of Natural numbers including zero. Determine whether the function given below is injective, surjective or bijective.
f N→N j2+2
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Define equivalence relation.
Let Z be the set of integers and R be the relation called "Congruence modulo 5"
defined by R − is divisible by Show that R is an equivalence relation. Determine the equivalence classes generated by the elements of Z.
07
OR
Q.4

Define Composition of a function. Let and and s be functions from X to X given by
p q
r s
Find oq qop, poroq, soq, qos, sos
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Find the inverse of the matrix
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Q.5

Define Tree. Draw a graph of tree represented by

Obtain a binary tree corresponding to it.
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Define adjacency matrix of a digraph. Obtain the adjacency matrix A of the
given digraph. Find the elementary paths of lengths 1 and 2 from v1 to v4 .
07
OR
Q.5

Give an abstract definition of graph. When are two simple graphs said to be
isomorphic? Give an example of two simple digraphs having 4 nodes and 4
edges which are not isomorphic
07

Define a unilateral component and strong component. Write unilateral and strong and weak components of the Graph given in following figure.
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