Term-End Examination
DecembeR, 2OO5
MCS-013 : DISCRETE MATHEMATICS
l. (a) Write The negaion of the folowing statements:
(i) For al x,x2 < x2=" 2." a =" {1," x4="9,whercx.">,i= 1,2,3,4.
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 ?
(b)Find the number of permuiations of the word ATTENDANT.
(c)Write the contrapositive of the statement 'If x is a positive real number, there is a number y
such that y2= x.'
3. (a) Given five points inside a square whose side has length 2, prove that two are within a distance of under root Z of each other.
(b)Prove. that ((p v q -> r) ^ (~p))-> (q -> r) is a tautology.
4. (a) A commitee of three individuals decides a proposal. Each individual votes either yes or no. The proposal is passed it receives atleast two votes. Design a circuit that determines whether ihe proposal pass
(b) Find the domain and range. of the function
-----
|1+x
| -----
\|1-X
where
(c)State whether the following statement is true or false, Give reasons for your answer.
"For any 3 sets A, B and C, and functions
f: A -> B, g: B -> C such that g of is surjective,
then f and g must be surjecive."
5.(a) How many boolean functions of n variables are there ? Give reasons for your answer.
(b)Check whether the folowing argument is valid, using a truth table.
"if Shalini leaves home belore 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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