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Posted By: S.Yamini       Member Level: Diamond       Posted Date: 08 May 2008
2005 Indira Gandhi National Open University (IGNOU) MCA Discrete Mathematics Question paper Course: MCA   University: Indira Gandhi National Open University (IGNOU) Test Papers / Previous Question Papers of IGNOU MCS13 Discrete Mathematics December 2005 MCA (Revised) Term-End Examination December, 2005 MCS-013 : DISCRETE MATHEMATICS Time: 2 hours Maximum Marks: 50 Note : Question number 1 is compulsory. Answer any three questions from the rest. 1. (a) Write the negation of the following statements : (2+2) (i) For all x, x2 < x. (ii) There exists x such that x2 = 2. (b) Construct the circuit that produces the following ourput : x' ^ (y v z')'. (4) (c) Let A = {1, 2, 3, 4, 5}. Construct a relation B from A to A such that R is reflexive and symmetric but not transitlve. (4) (d) Prove by induction that n3 - n is divisible by 3 for all positive integers. (4) (e) Determine all the integer solutions to x1 +x2 + x3+ x4= 9, where x = 1 , i = 1, 2, 3, 4. (4) 2. (a) A sequence of ten bits (0's and 1's) is randomly generated. What is the probability that at least one of the bits is 0 ? (5) Find the number of permutations of the word ATTENDANT. (3) Write the contrapositive of the statement 'If x is a positive real number, there is a number y such that y2 = x.' (2) 3. (a) Given five points inside a square whose side has length 2, prove that two are within a distance of v2 of each other. (5) (b) Prove that ((p v q ? r) ^ (~P)) ? (q ? r) is a tautology. (5) 4. (a) A committee of three individuals decides a proposal. Each individual votes elther yes or no. The proposal is passed if it receives at least two yes votes. Design a circuit that determines whether the proposal passes. (5) (b) Find the domain and range of the function v1+x/1-x, where x takes real values. (3) (c) State whether the following statement is true or false, Give reasons for your answer. (2) "For any 3 sets A, B and C, and functions f: A ? B, g: B ? C such that g o f is surjective, their f and g must be surjective." 5. (a) How many boolean functions of n variables are there ? Give reasons for your answer. (4) (b) Check whether the following argument is valid, using a truth table. (6) "lf Shalini leaves home before 9.00 AM or if she takes a taxi, she will reach office in time. She did leave after 10.00 AM and she did reach office in time. Therefore, Shalini must have taken a taxi. Return to question paper search
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