Exam Details
| Subject | discrete mathematical structures | |
| Paper | ||
| Exam / Course | b.tech | |
| Department | ||
| Organization | Institute Of Aeronautical Engineering | |
| Position | ||
| Exam Date | December, 2017 | |
| City, State | telangana, hyderabad |
Question Paper
Hall Ticket No Question Paper Code: AHS013
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech III Semester End Examinations (Regular) December, 2017
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. List and explain the Well-formed Formulas and Equivalent Formulas.
Verify the following logical equivalences using truth tables
i.
ii.
2. Verify the validity of the following argument. Tigers are dangerous animals. There are Tigers.
Therefore there are dangerous animals.
Show that R!S is a valid conclusion from the premises P P and Q.
UNIT II
3. Define the following and give suitable examples for each
i. Lattice
ii. Sub lattice
iii. Distributive lattice
iv. Complemented lattice
Let A be the given finite set and is its power set. Let be the inclusion relation on the
elements of Draw the Hasse diagrams of for
i.
ii.
iii.
iv.
4. Let n be a positive integer and Sn be the set of all divisors of n. let D denote the relation of
"division". Draw the diagrams of lattices for n 24 and 30.
Consider x-2 and 3x for x2R, where R is the set of real numbers.
Find hof(x) and fohog(x).
Page 1 of 3
UNIT III
5. Define Monoid and prove that identity element in a monoid is unique.
Prove the Pascal's identity
6. Find the term containing x8 in the expansion of
x2 2
x2
8.
Determine the number of non negative integral solutions of the equation
x1 x2 x3 x4 x5 18 where each xi 2.
UNIT IV
7. Solve the recurrencerelation using generating functions an 0 where
a0 10, a1 41
Find the solution of the recurrence relation using characteristic roots
an 0 where a0 a1 5
8. Find the solution of an n a0 a1 16
3 by the method of
Characteristic roots.
Find the coefficient of x18 in the product x2 x3 x4 x5)(x2 x3
UNIT V
9. Define the following and provide suitable example for each
i. Isomorphic graph
ii. Euler graph
iii. Hamiltonian Graph
iv. Planar Graph
Find a minimal spanning tree for the graph shown in Figure 1.
Figure 1
10. Define
i. Complete graph
ii. Bipartite graph with an example for each
Page 2 of 3
Is the following pair of graphs shown in Figure 2 isomorphic? Justify your answer
Figure 2
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech III Semester End Examinations (Regular) December, 2017
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. List and explain the Well-formed Formulas and Equivalent Formulas.
Verify the following logical equivalences using truth tables
i.
ii.
2. Verify the validity of the following argument. Tigers are dangerous animals. There are Tigers.
Therefore there are dangerous animals.
Show that R!S is a valid conclusion from the premises P P and Q.
UNIT II
3. Define the following and give suitable examples for each
i. Lattice
ii. Sub lattice
iii. Distributive lattice
iv. Complemented lattice
Let A be the given finite set and is its power set. Let be the inclusion relation on the
elements of Draw the Hasse diagrams of for
i.
ii.
iii.
iv.
4. Let n be a positive integer and Sn be the set of all divisors of n. let D denote the relation of
"division". Draw the diagrams of lattices for n 24 and 30.
Consider x-2 and 3x for x2R, where R is the set of real numbers.
Find hof(x) and fohog(x).
Page 1 of 3
UNIT III
5. Define Monoid and prove that identity element in a monoid is unique.
Prove the Pascal's identity
6. Find the term containing x8 in the expansion of
x2 2
x2
8.
Determine the number of non negative integral solutions of the equation
x1 x2 x3 x4 x5 18 where each xi 2.
UNIT IV
7. Solve the recurrencerelation using generating functions an 0 where
a0 10, a1 41
Find the solution of the recurrence relation using characteristic roots
an 0 where a0 a1 5
8. Find the solution of an n a0 a1 16
3 by the method of
Characteristic roots.
Find the coefficient of x18 in the product x2 x3 x4 x5)(x2 x3
UNIT V
9. Define the following and provide suitable example for each
i. Isomorphic graph
ii. Euler graph
iii. Hamiltonian Graph
iv. Planar Graph
Find a minimal spanning tree for the graph shown in Figure 1.
Figure 1
10. Define
i. Complete graph
ii. Bipartite graph with an example for each
Page 2 of 3
Is the following pair of graphs shown in Figure 2 isomorphic? Justify your answer
Figure 2
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