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Code No: NR210501

1. (a) Write the following statement in symbolic form: “The crop will be destroyed if there is a flood”

2. (a) List all the permutations on A = {a,b,c}

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(b) Construct the truth table of the following formula. ← ((PVQ) ∧ (PVR)) e (PV(Q ∧ R)) →

in

II B.Tech I Semester Supplimentary Examinations, May/Jun 2009 DISCRETE STRUCTURES AND GRAPH THEORY ( Common to Computer Science & Engineering, Information Technology and Electronics & Computer Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

[8+8]

[4+12]

or

(b) Let X= {1,2,3, ??.. ,25} and R= { (x,y) / x-y is divisible by 5 } be a relation on X. Show that R is an equivalence relation.

3. (a) Show that the function f(x) = x3 and g(x) = x1/3 for x∈R are inverse of each other [8+8] (b) Show that { < x, x > /x ∈ N} which defines the relation of equality is primitive recursive.

(b) Are  0  0 1

uW

4. (a) Use Warshall’s algorithm to find the transitive closure of the relation [10+6] R = {(1, 2)(1, 3)(1, 4)(2, 3)(2, 4)(3, 4)} the 0 0 1

simple   graphs with the following adjacency matrices isomorphic? 1 0 1 1   1 1 0 0  0 1 0 0

nt

5. (a) Prove that the Kuratowskis second graph consisting of 6 vertices and 9 edges is non-planar. (b) State criteria to detect the planarity of a connected graph and give an example also. [8+8]

Aj

6. Prove whether it is always, never, or some times the nodes are added to the minimum spanning tree by the Dijkstra-Prim algorithm is the same as the order in which they are encountered in a breadth-first traversal. [16] 7. (a) How many ways can 20 similar books be placed on 5 different shelves ? [8+8] (b) Enumerate the number of ways of placing 20 indistinguishable balls into 5 boxes where each box is nonempty.

8. Explain the Recurrence relation. What is its application in computer science explain with suitable examples. [16] ????? 1 of 1