IGNOU MCA -mcs-013 solved assignments 2012 -2013

Course Code : MCS-013

Course Code : MCS-013
Course Title : Discrete Mathematics
Assignment Number : MCA(1)/013/Assign/2012
Assignment Marks : 100
Weightage : 25%
Last Dates for Submission : 15th October, 2012 (For July 2012 Session)
15th April, 2013 (For January 2013 Session)

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 + 3 +4)
a) Make truth table for followings:

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 (3 + 3+3)
a) What is proof? Explain method of direct proof with the help of one example.
b) Show whether
11
is rational or irrational.
c) Prove that A - (A - B) : A

B
Question 3: Marks (4 + 4+ 4)
a) Set X has 10 members, how many members do P(X) has ? How many
members of P(X) are proper subset of X ?
b) Establish the equivalence: (P  Q)  (P  Q)

(~P + Q)  (Q  P)
c) If p an q are statements, show whether the statement [(~p→q)  (q)] → (p  q)
is a tautology or not.
9
Question 4: Marks (4 + 3 +3)
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 the followings
i. A - (A-B)
ii. A

B C
iii. A\B
Question 5: Marks (4+4 +2)
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, -1) x (3, -3)
c) Explain the concept of counterexample with the help of an example.
Question 6: Marks (5+4)
a) What is inclusion-exclusion principle? Explain inclusion-exclusion
principle with an example.
10
b) Find inverse of the following functions
i) f(x) =
353xx
3x
ii) f(x) =
4723xx
2x
Question 7: Marks (3 + 3 + 3)
a) Find how many 3 digit numbers are even? How many 3 digit numbers are composed of odd digits.
b) How many different 20 persons committees can be formed each containing at least 2 Professors and at least 3 Associate Professor from a set of 10 Professors and 42 Associate Professors.
c) Prove that for every positive integer n, n3 + n is even.
Question 8: Marks (4 +4 +2)
a) What is Demorgan‟s Law? Explain the use of Demorgen‟s law with an example?
b) How many ways are there to distribute 10 district object into 4 distinct boxes with
i) At least two empty box.
ii) No empty box.
c) In a fifty question true false examination a student must achieve twenty five correct answers to pass. If student answer randomly what is the probability that student will fail.

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Sunday, August 12, 2012

IGNOU MCA -mcs-013 solved assignments 2012 -2013

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