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TAMIL NADU OPEN UNIVERSITY MCA - I (SEM 2) JUN 2008 : Theory Of Computer Science

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Wk 6 MCA 650 MCA-10/ PGDCA-08 M.C.A./P.G.D.C.A. DEGREE/DIPLOMA EXAMINATION JUNE 2008. First Year/Second Semester THEORY OF COMPUTER SCIENCE Time : 3 hours Maximum marks : 75 Answer for 5 marks questions should not exceed 2 pages. Answer for 10/15 marks questions should not exceed 5 pages. PART A (5 5 = 25 marks) Answer any FIVE questions. 1. Define equivalence relation. Give examples. 2. If f ( x ) x 2, g( x ) f g, g f , f f and g g . x 2 for x R find 3. Construct truth table for ( P Q ) 7P . 4. Explain conjunctive and disjunctive normal forms. Wk 6 5. What examples. are isomorphic graphs? Explain with 6. Prove that sum of degrees of all vertices of a graph is equal to twice the number of edges in the graph. 7. Explain matrix representation of graphs with examples. PART B (5 10 = 50 marks) Answer any FIVE questions. 8. Let X R {1, 2, 3, 4} and {( x, y) / x y} be a relation on X. Determine properties of R and also write the relation matrix. 9. Prove that transitive closure R+ of a relation R in a finite set X is transitive. 10. Construct truth (Q ( P Q )) P. 11. Show that R the premises P (P Q, Q table for the formula Q ) is a valid conclusion from R, P M and M. 12. Construct a turing machine T { A, Q, X , P } in which A {a, b, B } with states Q { qi (0 i n )} . 2 MCA 650 Wk 6 13. Prove that in a simple digraph G node lies in exactly one string component. (V , E ) every 14. Show that in a complete binary tree the total number of edges is (2n 1) where n is number of terminal nodes. 3 MCA 650

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Additional Info : Mca - I (sem 2) June 2008 Question Paper - Theory Of Computer Science
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