Exam Details

Subject discrete mathematical structures
Paper
Exam / Course b.tech
Department
Organization Institute Of Aeronautical Engineering
Position
Exam Date November, 2018
City, State telangana, hyderabad


Question Paper

Hall Ticket No Question Paper Code: AHS013
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Four Year B.Tech III Semester End Examinations (Regular) November, 2018
Regulation: IARE R16
DISCRETE MATHEMATICAL STRUCTURES
Time: 3 Hours (Common to CSE IT Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Show that is a Tautology using truth table.
Show that the statement "Every positive integer is the sum of squares of three integers" is false.

2. Construct the truth table for the formula (PV V :P.
Explain about the tautological implications and logical equivalence using theorem.
UNIT II
3. Show that a relation R defined on the set of real numbers as R if a2 b2 c2 d2.
Show that R is an equivalence relation.
Let Draw the diagram of the graph R and also give its matrix.

4. Illustrate the following function definition with graph. Let X and Y be any two sets. A relation f
from X to Y is called a function if for every x2X there is a unique y2Y such that
Let and Also let f:X→Y be and g:Y→Z be
given by Find gof.
UNIT III
5. Show that the intersection of any two congruence relations on a set is also a congruence relation.

Let and be the algebraic system. Show that is a homomorphic image of

Page 1 of 2
6. Prove using the theorem by showing that the composition of semi group homomorphism is also
a semi group homomorphism.
Let be the algebraic system of natural numbers. Define an equivalence relation E on N
such that x1 Ex2 iff either x1-x2 or x2-x1 is divisible by 4. Show that E is a congruence relation
and that the homomorphism g defined is the natural homomorphism associated with E.
UNIT IV
7. What is the solution of the recurrence relation an for n 2 given that a0
a1 6.
Find the recurrence relation for the Fibonacci sequence.
8. A computer system considers a string of decimal digits a valid codeword if it contains an even
number of 0 digits. For instance, 1230407869 is valid, whereas 120987045608 is not valid. Let an
be the number of valid n-digit codeword's. find the recurrence relation for an.
Find r recurrence relation for Cn, the number of ways to parenthesize the product of n+1 numbers,
x0, x1x2…xn, to specify the order of multiplication. For example, C3=5 because there are five ways
to parenthesize x0, x1x2 x3 to determine the order of multiplication: ((x0.x1)x2).x3 (x0.(x1)x2).x3
(x0. x1) x0.((x1)x2).x3) x0. (x1 (x2 .x3)).
UNIT V
9. Prove that if G is connected graph with n vertices and edges then G is a tree.
Show that the graphs G and H displayed in following Figure 1 are isomorphic.
Figure 1
10. Prove that the chromatic number of a tree is always 2 chromatic polynomial is

Show that neither graph displayed in following Figure 2 has a Hamilton circuit.


Subjects

  • ac machines
  • advanced databases
  • aircraft materials and production
  • aircraft performance
  • aircraft propulsion
  • aircraft systems and controls
  • analog communications
  • analysis of aircraft production
  • antennas and propagation
  • applied physics
  • applied thermodynamics
  • basic electrical and electronics engineering
  • basic electrical engineering
  • building materials construction and planning
  • business economics and financial analysis
  • compiler design
  • complex analysis and probability distribution
  • computational mathematics and integral calculus
  • computer networks
  • computer organization
  • computer organization and architecture
  • computer programming
  • concrete technology
  • control systems
  • data structures
  • database management systems
  • dc machines and transformers
  • design and analysis of algorithms
  • design of machine members
  • digital and pulse circuits
  • digital communications
  • digital ic applications using vhdl
  • digital logic design
  • digital system design
  • disaster management
  • disaster management and mitigation
  • discrete mathematical structures
  • dynamics of machinery
  • electrical circuits
  • electrical measurements and instrumentation
  • electrical technology
  • electromagnetic field theory
  • electromagnetic theory and transmission lines
  • electronic circuit analysis
  • electronic devices and circuits
  • elements of mechanical engineering
  • engineering chemistry
  • engineering drawing
  • engineering geology
  • engineering mechanics
  • engineering physics
  • english
  • english for communication
  • environmental studies
  • finite element methods
  • fluid mechanics
  • fluid mechanics and hydraulics
  • fundamental of electrical and electronics engineering
  • fundamental of electrical engineering
  • gender sensitivity
  • geotechnical engineering
  • heat transfer
  • high speed aerodynamics
  • hydraulics and hydraulic machinery
  • image processing
  • industrial automation and control
  • instrumentation and control systems
  • integrated circuits applications
  • introduction to aerospace engineering
  • kinematics of machinery
  • linear algebra and calculus
  • linear algebra and ordinary differential equations
  • low speed aerodynamics
  • machine tools and metrology
  • mathematical transform techniques
  • mathematical transforms techniques
  • mechanics of fluids and hydraulic machines
  • mechanics of solids
  • mechanism and machine design
  • metallurgy and material science
  • microprocessor and interfacing
  • modern physics
  • network analysis
  • object oriented analysis and design
  • object oriented programming through java
  • operating systems
  • optimization techniques
  • power electronics
  • power generation systems
  • probability and statistics
  • probability theory and stochastic processes
  • production technology
  • programming for problem solving
  • pulse and digital circuits
  • reinforced concrete structures design and drawing
  • software engineering
  • strength of materials - i
  • strength of materials - ii
  • structural analysis
  • surveying
  • theory of computation
  • theory of structures
  • thermal engineering
  • thermo dynamics
  • thermodynamics
  • tool design
  • transmission and distribution systems
  • unconventional machining processes
  • waves and optics
  • web technologies