Course Code : MCS-013
Course Title : Discrete Mathematics
Assignment Number : MCA(1)/013/Assign/2011
Assignment Marks : 100
Weightage : 25%
Last Date of Submission : 15th April,2011 (for January session)
15th October, 2011 (for July session)
BCA MCA Bsc B tech CS information technology
final year project
There are eight questions in this assignment, which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.
Question 1:
Marks ( 4 + 4 +4)
a) Make truth table for
i) ~p→(q ~ r) ~p q
ii) ~p→r ~q ~p ~r
b) What are conditional connectives? Explain use of conditional connectives with an example.
c) Write down suitable mathematical statement that can be represented by the following symbolic properties.
i) ( x) ( y) ( z) P
ii) (x) ( y) ( z) P
Question 2:
Marks (4 + 4)
a) What is proof? Explain method of direct proof with the help of one example.
b) Show whether is rational or irrational.
Question 3:
Marks (5 + 5)
a) What is Boolean algebra? Explain how Boolean algebra methods are used in logic circuit design.
b) If p an q are statements, show whether the statement [(~p→q) (q)] → (p ~q)
is a tautology or not.
Question 4:
Marks (4 + 4 +2)
a) Make logic circuit for the following Boolean expressions:
i) (x′.y + z) + (x+y+z)′ +(x+y+z)
ii) ( x'+y).(y′+ z).(y+z′+x′)
b) What is dual of a Boolean expression? Find dual of boolean expression of the
output of the following logic circuit:
c) Set A,B and C are:
A = {1, 2, 3, 4, 5,6,9,19,15}, B = { 1,2,5,22,33,99 } and C { 2, 5,11,19,15},
Find A B C and A B C
Question 5: Marks (3+4 +4)
a) Draw a Venn diagram to represent followings:
i) (A B) (C~B)
ii) (A B) (B C)
b) Give geometric representation for following
i) R x { 3}
ii) {-1, -2) x (-3, -3)
c) What is counterexample? Explain the use of counterexample with the help of an example.
Question 6:
Marks (5+4)
a) What is inclusion-exclusion principle? Also explain one application of inclusion-exclusion principle.
b) Find inverse of the following functions
i) f(x) =
ii) f(x) =
Question 7:
Marks ( 4 + 3 + 3)
a) Find how many 4 digit numbers are even? How many 4 digit numbers are composed of odd digits.
b) How many different 15 persons committees can be formed each containing at least
2 Accountants and at least 3 Managers from a set of 10 Accountants and 12 Managers.
c) What is a function? Explain one to one mapping with an example.
Question 8:
Marks ( 4 +4 +2)
a) What is Demorgan’s Law? Also explain the use of Demorgen’s law with example?
b) How many ways are there to distribute 15 district object into 5 distinct boxes with
i) At least two empty box.
ii) No empty box.
c) In a fifteen question true false examination a student must achieve five correct
answers to pass. If student answer randomly what is the probability that student will fail.
Course Title : Discrete Mathematics
Assignment Number : MCA(1)/013/Assign/2011
Assignment Marks : 100
Weightage : 25%
Last Date of Submission : 15th April,2011 (for January session)
15th October, 2011 (for July session)
BCA MCA Bsc B tech CS information technology
final year project
There are eight questions in this assignment, which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.
Question 1:
Marks ( 4 + 4 +4)
a) Make truth table for
i) ~p→(q ~ r) ~p q
ii) ~p→r ~q ~p ~r
b) What are conditional connectives? Explain use of conditional connectives with an example.
c) Write down suitable mathematical statement that can be represented by the following symbolic properties.
i) ( x) ( y) ( z) P
ii) (x) ( y) ( z) P
Question 2:
Marks (4 + 4)
a) What is proof? Explain method of direct proof with the help of one example.
b) Show whether is rational or irrational.
Question 3:
Marks (5 + 5)
a) What is Boolean algebra? Explain how Boolean algebra methods are used in logic circuit design.
b) If p an q are statements, show whether the statement [(~p→q) (q)] → (p ~q)
is a tautology or not.
Question 4:
Marks (4 + 4 +2)
a) Make logic circuit for the following Boolean expressions:
i) (x′.y + z) + (x+y+z)′ +(x+y+z)
ii) ( x'+y).(y′+ z).(y+z′+x′)
b) What is dual of a Boolean expression? Find dual of boolean expression of the
output of the following logic circuit:
c) Set A,B and C are:
A = {1, 2, 3, 4, 5,6,9,19,15}, B = { 1,2,5,22,33,99 } and C { 2, 5,11,19,15},
Find A B C and A B C
Question 5: Marks (3+4 +4)
a) Draw a Venn diagram to represent followings:
i) (A B) (C~B)
ii) (A B) (B C)
b) Give geometric representation for following
i) R x { 3}
ii) {-1, -2) x (-3, -3)
c) What is counterexample? Explain the use of counterexample with the help of an example.
Question 6:
Marks (5+4)
a) What is inclusion-exclusion principle? Also explain one application of inclusion-exclusion principle.
b) Find inverse of the following functions
i) f(x) =
ii) f(x) =
Question 7:
Marks ( 4 + 3 + 3)
a) Find how many 4 digit numbers are even? How many 4 digit numbers are composed of odd digits.
b) How many different 15 persons committees can be formed each containing at least
2 Accountants and at least 3 Managers from a set of 10 Accountants and 12 Managers.
c) What is a function? Explain one to one mapping with an example.
Question 8:
Marks ( 4 +4 +2)
a) What is Demorgan’s Law? Also explain the use of Demorgen’s law with example?
b) How many ways are there to distribute 15 district object into 5 distinct boxes with
i) At least two empty box.
ii) No empty box.
c) In a fifteen question true false examination a student must achieve five correct
answers to pass. If student answer randomly what is the probability that student will fail.
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