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Posted Date: 29 Nov 2008 Posted By: hari Member Level: Gold
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2005 Jawaharlal Nehru Technological University Information Technology II B.Tech. I Semester Supplementary Examinations, May -2005 DISCRETE STRUCTURES AND GRAPH THEORY Question paper
Code No: RR210501 Set No.1
II B.Tech. I Semester Supplementary Examinations, May -2005
DISCRETE STRUCTURES AND GRAPH THEORY
( Common to Computer Science & Engineering, Information Technology,
Computer Science & Systems Engineering and Electronics & Computer
Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Describe the Tautological implications
(b) Show the following implications without constructing the truth table.
P ! Q ) P! (P ^ Q)
2. (a) Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the following relation R on A
such that (a, b) R (a’, b’) if and only if a b’ = a’b.
(b) Show that R is an equivalence relation.
(c) Compute A/R.
3. (a) Define the term ‘lattice’, clearly stating the axioms.
(b) Let C be a collection of sets which are closed under intersection and union.
Verify whether (C, \, [) is a lattice.
4. Prove that any 2 simple connected graphs with n vertices, all of degree 2, are
isomorphic.
5. Suppose that (X,X) is an S-D cut in a transport net work (G, K). Prove that (X,X)
and (X, X) contain an equal number of edges in common with any directed circuit
in G.
6. Prove whether it is always, never, or some times prove that the order in which 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 depth-first traversal.
7. (a) How many integral solutions are there to x1 + x2 + x3 + x4 + x5 = 20 where
each xi 2 ?
(b) Find the number of district triples (x1, x2, x3) of nonnegative integers satisfying
the inequality x1 + x2 + x3 < 6.
8. Solve the recurrence relation
S(k) - 0.25 S(k-1) = 0, S(o) = 6.
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