DATA STRUCTURE and sets, Exam paper, UPTU 2007, Exams of Data Structures and Algorithms

Download DATA STRUCTURE and sets, Exam paper, UPTU 2007 and more Exams Data Structures and Algorithms in PDF only on Docsity! UNUM Printed Pages : 4 MCA-244(2) (Following Paper ID and Roll No. to be filled in your Answer Book) PBEM FolN TTT LELLLL M. C. A. (SEM. TV) EXAMINATION, 2006 - 2007 DISCRETE STRUCTURES Time : 3 Hours] {Total Marks : 100 Note : Answer all questions. All questions carry equal marks. 1 Answer any four of the following : 5x4=20 (a) For any sets A and B prove (AUB) = AS ABS Q) (ANB) = AS UBS (b) In a group of 52 persons who drink tea or coffee or both, 16 drink tea but not coffee and 33 drink tea. Find how many (@) drink tea and coffee both (ii) drink coffee but not tea. (©) A relation R on the set A= fi, 2, 3, 4} given by R=[G, D), G, 2, 2 YD, BD, BB, G3), 4, 2B 4 4] Tepresent it by a diagraph and indegrees and outdegrees of each vertex. (d) Prove that the intersection of two equivalence relation is also an equivalence relation, but the union of two equivalence relation may not be an equivalence relation. V-1459] 1 [Contd... (e) Let f:A>B and g: BC be two invertible mapping then prove (1) — gof is invertible @ (gofy* =f tog” («If f and g be functions defined on the set of real numbers by F(x)=x+1, g(x) =" 42. find (1) gof(-2) (2) fog(-2) (3) gof(x) 4) fog(x) 6) gog(x). 2 Answer any two of the following : 10x2=20 (a) Let A, ={x : x is divisible by n} where pe N. Find Ayn A, and AU Ay. (b) Prove that conditional operation distributes over conjunction, ie. p> (avv)=(p > g)v(p > v) (c) Show that the statement (pagd=>(@va) is a tautology, but (pv q@ > (pq) is not. 3 Answer any two of the following : 10x2=20 @ Tf *P 43 4p, =30,800 : 1, find the value of r. V-1459] 2 [Contd...