MCS-013 Discrete Mathematics
Course Code : MCA(1)/013/Assign/09
Last Dates for Submission : 15th April, 2009 (For January Session) 15th October, 2009 (For July Session)
Max. Marks: 100 Weightage:25%
There are eight questions in this assignment. Answer all questions. 20 Marks are for viva-voce.
Note : Attempt all Questions.
Q1.
(a) . Make truth table for :
i) q?(p ~ r) p q
ii) p?q q p ~ r (4 Marks)
(b). Explain with example the use of conditional connectives in the forming of prepositions.
(2 Marks)
(c). Write down suitable mathematical statement that can be represented by the following symbolic properties.
i). ( x) ( y) P
ii). (x) ( y) ( z) P (4 Marks)
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Q2.
(a). Explain different methods of proof with the help of one example of each. (6 Marks)
(b). Show whether root 17 is rational or irrational. (4 Marks)
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Q3.
(a). What is Boolean algebra? Write uses of Boolean algebra. Explain how you can find dual of a theorem about Boolean algebra. (5 Marks)
(b). If p and q are statements, show whether the statement [(p?q) (~ q)] ? (~p) is a tautology or not. (5 Marks)
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Q4.
(a). Make logic circuit for the following Boolean expressions:
i). (x.y + z) + (x+z)
ii). x.y?+ y.z?+z?x? + x .y (4 Marks)
(b). Find Boolean expression for the output of the following logic circuit given in the Figure a:
(3 Marks)
(c). Write a superset for the following sets:
A = {1, 2, 3, 4, 9, 19}, B = {1, 2} and
C {2, 5, 11}, D = {1, 3, 5}
Also tell whether set B is a subset of set C or not. (3 Marks)
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Q5.
(a). Draw a Venn diagram to represent followings:
i) (A B) (C~A)
ii) (A B) (B C) (4 Marks)
(b). Give geometric representation for the following:
i) { 3, 1} x R
ii) {-1, -1) x ( -2, 3) (4 Marks)
(c). What is principle of strong mathematical induction? In which situation this principle is used. (2 Marks)
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Q6.
(a). What is permutation? Explain circular permutation with example. (5 Marks)
(b). Find inverse of the following function:
(2 Marks)
(c). What is a function? Explain the uses of the functions. (3 Marks)
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Q7.
(a). How many 4 digits number can be formed from 6 digits 1, 2, 3, 4, 5 ,6 if repetitions are not allowed. How many of these numbers are less than 4000? How many are odd? (5 Marks)
(b). What is pigeonhole principle? Explain the applications of pigeonhole principle with example? (5 Marks)
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Q8.
(a). How many different 5 persons committees can be formed each containing at least two women and at least one man from a set of 10 women and 15 men. (3 Marks)
(b). How many ways are there to distribute or district object into 12 distinct boxes with
i) At least three empty box.
ii) No Empty box. (4 Marks)
(c). In a twenty question true false examination a student must achieve eight correct answers to pass. If student answer randomly what is the probability that student will fail. (3 Marks)
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