Exam Details
Subject | discrete mathematical structures | |
Paper | ||
Exam / Course | b.tech | |
Department | ||
Organization | Institute Of Aeronautical Engineering | |
Position | ||
Exam Date | February, 2018 | |
City, State | telangana, hyderabad |
Question Paper
Hall Ticket No Question Paper Code: AHS013
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech III Semester End Examinations (Supplementary) February, 2018
Regulation: IARE R16
DISCRETE MATHEMATICAL STRUCTURES
(Common for CSE IT)
Time: 3 Hours 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 T.
Explain the principal disjunctive and principal conjunctive normal forms and obtain the principal
disjunctive normal form of R).
2. State Tautology and Contradiction. Verify whether the implications are Tautology or Contradiction
using truth tables.
i.[P
ii.
Explain the steps involved in principal conjunctive normal form and obtain the principal Conjunctive
normal form of R).
UNIT II
3. Define the following properties of binary relation with suitable examples reflexive, symmetric,
transitive, ir-reflexive and anti-symmetric
Let be a lattice, and be two operations such that a b glb fa; bg ab lub fa; bg.
Prove that both and satisfy Commutative law, Associative law, Absorption law and Idempotent
law.
4. If the relations R and S are compatibility relations, prove that R S is compatibility relation.
Let P 12 and be the relation on P such that x y if and only if x divides
y. Draw the Hasse diagram for the poset
UNIT III
5. Suppose that the license plates of a certain staterequire3 English letters followed by 4 digits,
i. How many different plates can be manufactured if repetition of letters and digits are allowed?
ii. How many plates are possible if only the letters can be repeated?
iii. How many are possible if only the digits can be repeated?
iv. How many are possible if no repetitions are allowed at all?
State Multinomial theorem and Find the coefficient of w2x2y2z2 in the expansion of
x y z 1)10
Page 1 of 3
6. Suppose that 200 faculty members can speak French and 50 can speak Russian, while only 20
can speak both French and Russian. How many faculty members can speak either French or
Russian? Use principle of inclusion-exclusion.
Find the term independent of x in the expansion of
x2 1
x
12.
UNIT IV
7. Find the coefficient of x14 in x x2 x3)10.
Find a particular solution to the following in homogeneous recurrence relation an
4nforn 2.
8. Find the complete solution to the homogeneous recurrence relation 4nforn
2.
Solve the recurrence relation an 2n 1 where a0=1 by substitution method.
UNIT V
9. Define with an example:
Euler circuit
Hamiltonian circuit
Is the following pair of graphs isomorphic? Justify your answer
Figure 1
10. Find the depth first spanning tree for the following graph is the order of the vertices is
i.
ii.
Figure 2
Page 2 of 3
Determine the chromatic number of the following graph. (Give a careful argument to show that
fewer colors will not suffice.)
Figure 3
Page 3 of 3
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech III Semester End Examinations (Supplementary) February, 2018
Regulation: IARE R16
DISCRETE MATHEMATICAL STRUCTURES
(Common for CSE IT)
Time: 3 Hours 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 T.
Explain the principal disjunctive and principal conjunctive normal forms and obtain the principal
disjunctive normal form of R).
2. State Tautology and Contradiction. Verify whether the implications are Tautology or Contradiction
using truth tables.
i.[P
ii.
Explain the steps involved in principal conjunctive normal form and obtain the principal Conjunctive
normal form of R).
UNIT II
3. Define the following properties of binary relation with suitable examples reflexive, symmetric,
transitive, ir-reflexive and anti-symmetric
Let be a lattice, and be two operations such that a b glb fa; bg ab lub fa; bg.
Prove that both and satisfy Commutative law, Associative law, Absorption law and Idempotent
law.
4. If the relations R and S are compatibility relations, prove that R S is compatibility relation.
Let P 12 and be the relation on P such that x y if and only if x divides
y. Draw the Hasse diagram for the poset
UNIT III
5. Suppose that the license plates of a certain staterequire3 English letters followed by 4 digits,
i. How many different plates can be manufactured if repetition of letters and digits are allowed?
ii. How many plates are possible if only the letters can be repeated?
iii. How many are possible if only the digits can be repeated?
iv. How many are possible if no repetitions are allowed at all?
State Multinomial theorem and Find the coefficient of w2x2y2z2 in the expansion of
x y z 1)10
Page 1 of 3
6. Suppose that 200 faculty members can speak French and 50 can speak Russian, while only 20
can speak both French and Russian. How many faculty members can speak either French or
Russian? Use principle of inclusion-exclusion.
Find the term independent of x in the expansion of
x2 1
x
12.
UNIT IV
7. Find the coefficient of x14 in x x2 x3)10.
Find a particular solution to the following in homogeneous recurrence relation an
4nforn 2.
8. Find the complete solution to the homogeneous recurrence relation 4nforn
2.
Solve the recurrence relation an 2n 1 where a0=1 by substitution method.
UNIT V
9. Define with an example:
Euler circuit
Hamiltonian circuit
Is the following pair of graphs isomorphic? Justify your answer
Figure 1
10. Find the depth first spanning tree for the following graph is the order of the vertices is
i.
ii.
Figure 2
Page 2 of 3
Determine the chromatic number of the following graph. (Give a careful argument to show that
fewer colors will not suffice.)
Figure 3
Page 3 of 3
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