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PUNJAB TECHNICAL UNIVERSITY MCA - I (SEM 1) MAY 2008 : Computer Mathematical Foundation

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Roll No. ........................... Total No. of Questions : 13] [Total No. of Pages : 03 Paper ID [A0504] (Please fill this Paper ID in OMR Sheet) MCA (104) (S05) (Old) (Sem. - 1st) COMPUTER MATHEMATICAL FOUNDATION Time : 03 Hours Maximum Marks : 75 Instruction to Candidates: 1) Section - A is Compulsory. 2) Attempt any Nine questions from Section - B. Section - A Q1) (15 2 = 30) a) State duality principle. b) Define Equivalence Relation and explain with example. c) Define with examples Square & Anti Symmetric Matrix. d) Prove that A B = (A B) (A B) e) Define Reflexive relation with example. f) Find Determinant of:019 830 213 g) List any 2 properties of determinants with example. h) Find Rank of matrix given below:3 1 3 2 4 3 3 1 1 i) Define Binary Tree and Directed Graph. j) What is Bipartite graph. D - 166 P.T.O. k) Define Path of a graph. l) Define Walk of a Graph. m) With Principle of Mathematical Induction Show that 2n>n for every n N . n) What do you mean by Tautology? o) What do you mean by Conditional operators? Section - B (9 5 = 45) Q2) Let R be a Relation in A = {6, 7, 1, 2, 3, 4, 5} defined by open sentence |x y| is divisible by 7 . Write R as a set of ordered pair. Q3) State and prove De Morgan s Law. Q4) If A, B, C are any three sets, then prove by taking any example that A (B C) = (A B) (A C) . xyz Q5) Find = y x z zyx Q6) Give an example of two square matrices of order 2 2 each so that (A + B) (A B) = 0. Q7) Using Gauss Jordan Method solve following question: 2x + 2y z = 3 2x y + 3z = 4 5x 3y + z = 3 Q8) Draw the Directed Graph whose adjacency matrix is given below: 0 1 0 1 D - 166 1 0 0 0 1 1 1 0 1 0 1 0 2 Q9) Find the Shortest Path Between a and d . Q10) State and Prove Hand Shaking theorem in Graphs. Q11) Prove by Principle of Mathematical Induction that for all n N: Sum of n Natural number is (n(n+1))/2. Q12) By using truth table Show that is Tautology. Q13) What do you mean by Universal and Existential Quantifiers. ZZZ D - 166 3

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Additional Info : Mca - I (sem 1) May 2008 Question Paper - Computer Mathematical Foundation
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