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Posted By: SRIMATHI Member Level: Diamond Posted Date: 27 Apr 2008
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2005 Indira Gandhi National Open University (IGNOU) M.C.A Discrete Mathematics Question paper
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2005 Indira Gandhi National Open University (IGNOU)
M.C.A Computer Science
MCS-013 : Discrete Mathematics Question paper
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.
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