Code: 13077

NR/RR

Set 1

1. a) Explain the following terms: i) Tautology and ii) contradiction. b) Show that (7 P∧ ( 7Q∧R)) ∨ (Q ∧ R) ∨ ( P ∧ R) ⇔ R

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 DISCRETE STRUCTURES & GRAPH THEORY (Common to CSE, CSIT, ECC) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

[8+8]

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2. a) Define the terms i) Equivalence relation, and ii) Partially order red sets. b) Let R = { (1, 2), (1, 4), (2, 3), (3, 4)} and S= { (2, 4), (2, 5), (3, 5)}. Find ROS and RO(SOR). [8+8] 3. a) Let f(x)= x2+2x+1, then find f(x+1). b) What is meant by invertible function? How to determine whether invertible function f -1 exists for the function f or not. [8+8]

uW

4. a) Define complete bipartite graph Km, n . b) Explain the steps involved in Warshal’s algorithm to find the transitive closure of a relation. [8+8] 5. a) Define i)cycle, ii) circuit and iii) path. b) What is the chromatic number of i) Tree ii) wheel graph iii) complete graph Kn and [8+8] iv) complete bipartite graph Km, n. 6. a) Distinguish between tree and spanning tree. b) Explain the steps involved in breadth first search traversal of a tree. Give an example. [8+8]

[8+8]

8. a) What are the applications of recurrence relations in computer science. b) Solve the recurrence relation n s (n+1) – s(n) =0, S(0)=1.

[8+8]

Aj

nt

7. a) In how many ways can a hand of 12 cards can be selected from a deck of S2 cards. b) How many integral solutions are there to x1 + x2 + x3 + x4 = 50 where each xi ≥ 4

************

Code: 13077

NR/RR

Set 2

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 DISCRETE STRUCTURES & GRAPH THEORY (Common to CSE, CSIT, ECC) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1. a) Let f(x)= x2+2x+1, then find f(x+1). b) What is meant by invertible function? How to determine whether invertible function f -1 exists for the function f or not. [8+8]

or ld

2. a) Define complete bipartite graph Km, n . b) Explain the steps involved in Warshal’s algorithm to find the transitive closure of a relation. [8+8] 3. a) Define i)cycle, ii) circuit and iii) path. b) What is the chromatic number of i) Tree ii) wheel graph iii) complete graph Kn and iv) complete bipartite graph Km, n. [8+8]

uW

4. a) Distinguish between tree and spanning tree. b) Explain the steps involved in breadth first search traversal of a tree. Give an example. [8+8] 5. a) In how many ways can a hand of 12 cards can be selected from a deck of S2 cards. b) How many integral solutions are there to x1 + x2 + x3 + x4 = 50 where each xi ≥ 4 [8+8]

[8+8]

7. a) Explain the following terms: i) Tautology and ii) contradiction. b) Show that (7 P∧ ( 7Q∧R)) ∨ (Q ∧ R) ∨ ( P ∧ R) ⇔ R

[8+8]

nt

6. a) What are the applications of recurrence relations in computer science. b) Solve the recurrence relation n s (n+1) – s(n) =0, S(0)=1.

Aj

8. a) Define the terms i) Equivalence relation, and ii) Partially order red sets. b) Let R = { (1, 2), (1, 4), (2, 3), (3, 4)} and S= { (2, 4), (2, 5), (3, 5)}. Find ROS and RO(SOR). [8+8] ************

Code: 13077

NR/RR

Set 3

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 DISCRETE STRUCTURES & GRAPH THEORY (Common to CSE, CSIT, ECC) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

1. a) Define i)cycle, ii) circuit and iii) path. b) What is the chromatic number of i) Tree ii) wheel graph iii) complete graph Kn and iv) complete bipartite graph Km, n. [8+8]

or ld

2. a) Distinguish between tree and spanning tree. b) Explain the steps involved in breadth first search traversal of a tree. Give an example. [8+8] 3. a) In how many ways can a hand of 12 cards can be selected from a deck of S2 cards. b) How many integral solutions are there to x1 + x2 + x3 + x4 = 50 where each xi ≥ 4 [8+8]

[8+8]

5. a) Explain the following terms: i) Tautology and ii) contradiction. b) Show that (7 P∧ ( 7Q∧R)) ∨ (Q ∧ R) ∨ ( P ∧ R) ⇔ R

[8+8]

uW

4. a) What are the applications of recurrence relations in computer science. b) Solve the recurrence relation n s (n+1) – s(n) =0, S(0)=1.

6. a) Define the terms i) Equivalence relation, and ii) Partially order red sets. b) Let R = { (1, 2), (1, 4), (2, 3), (3, 4)} and S= { (2, 4), (2, 5), (3, 5)}. Find ROS and RO(SOR). [8+8]

nt

7. a) Let f(x)= x2+2x+1, then find f(x+1). b) What is meant by invertible function? How to determine whether invertible function f -1 exists for the function f or not. [8+8]

Aj

8. a) Define complete bipartite graph Km, n . b) Explain the steps involved in Warshal’s algorithm to find the transitive closure of a relation. [8+8] ************

Code: 13077

NR/RR

Set 4

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 DISCRETE STRUCTURES & GRAPH THEORY (Common to CSE, CSIT, ECC) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

1. a) In how many ways can a hand of 12 cards can be selected from a deck of S2 cards. b) How many integral solutions are there to x1 + x2 + x3 + x4 = 50 where each xi ≥ 4 [8+8]

[8+8]

3. a) Explain the following terms: i) Tautology and ii) contradiction. b) Show that (7 P∧ ( 7Q∧R)) ∨ (Q ∧ R) ∨ ( P ∧ R) ⇔ R

[8+8]

or ld

2. a) What are the applications of recurrence relations in computer science. b) Solve the recurrence relation n s (n+1) – s(n) =0, S(0)=1.

uW

4. a) Define the terms i) Equivalence relation, and ii) Partially order red sets. b) Let R = { (1, 2), (1, 4), (2, 3), (3, 4)} and S= { (2, 4), (2, 5), (3, 5)}. Find ROS and RO(SOR). [8+8] 5. a) Let f(x)= x2+2x+1, then find f(x+1). b) What is meant by invertible function? How to determine whether invertible function f -1 exists for the function f or not. [8+8] 6. a) Define complete bipartite graph Km, n . b) Explain the steps involved in Warshal’s algorithm to find the transitive closure of a relation. [8+8]

nt

7. a) Define i)cycle, ii) circuit and iii) path. b) What is the chromatic number of i) Tree ii) wheel graph iii) complete graph Kn and iv) complete bipartite graph Km, n. [8+8]

Aj

8. a) Distinguish between tree and spanning tree. b) Explain the steps involved in breadth first search traversal of a tree. Give an example. [8+8] ************