Course Code

:

MCS013

Course
Title

:

Discrete
Mathematics

Assignment
Number

:

MCA(I)/013/Assignment/1516

Maximum Marks

:

100

Weightage

:

25%

Last Dates for
Submission

:

15^{th} October, 2015 (For July 2015
Session)

15^{th} April, 2016 (For January 2016 Session)

There are eight questions in this
assignment, which carries 80 marks. Rest 20 marks are for vivavoce. 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.
1. (a)
Make truth table for followings.

(4 Marks)


i) p→(~q

~ r)

~p

~q


ii)
p→(r

~ q)

(~p

r)


(b) Draw a venn diagram to represent
followings:

(3 Marks)


i)

(A

B)

(C~A)


ii)

(A

B)

(B

C)


(c) Give geometric representation for
followings:

(3 Marks)

i)
{
2} x R
ii)
{1,
2) x ( 2, 3)
2.

(a) Write down suitable mathematical statement
that can be represented

(4 Marks)


by the following symbolic
properties.


(i) (

x)
(

y) P


(ii)

(x)
(

y) ( z) P


(b) Show whether √15 is rational or irrational.

(4 Marks)


(c) Explain inclusionexclusion principle with
example.

(2 Marks)


3.

(a) Make logic circuit for the following
Boolean expressions:

(6 Marks)

i)
(x’
y’ z) + (xy’z)’
ii)
(
x'y) (yz’) (y’z)
iii)
(xyz)
+(xy’z)
(b) What is a tautology? If P and Q are
statements, show whether the (4
Marks)
statement
is a
tautology or not.
4.

(a)

How many different 8
professionals committees can be formed each

(4 Marks)

containing at least 2
Professors, at least 2 Technical Managers and 3


Database
Experts from list of 10 Professors, 8 Technical Managers


and 10 Database Experts?


(b)

What are Demorgan’s Law?
Explain the use of Demorgen’s law with

(4 Marks)


example.


(c)

Explain addition theorem in
probability.

(2 Marks)


5.

(a)

How many words can be formed
using letter of UNIVERSITY using

(2 Marks)

each letter at
most once?

i)
If
each letter must be used,
ii)
If
some or all the letters may be omitted.
(b) Show that:

(4 Marks)


(c)

Prove that n! (n + 2) = n!+ (n
+1)!

(4 Marks)

6. (a)

How many ways are there to
distribute 20 district object into 10

(3 Marks)

distinct boxes with:

i)
At
least three empty box.
ii)
No
empty box.
(b) Explain principle of multiplication with an
example.

(3
Marks)


(c)

Set A,B and C are: A = {1, 2,
4, 8, 10 12,14}, B = { 1,2, 3 ,4, 5 }

(4
Marks)


and C { 2,
5,7,9,11, 13}.


Find A

B

C , A B
C, A B C and (B~C)


7.

(a)

Find how many 3 digit numbers
are odd?

(2
Marks)


(b)

What is counterexample? Explain
with an example.

(3
Marks)


(c) What is a function? Explain following types
of functions with example

(5
Marks)


i) Surgective ii) Injective
iii) Bijective


8.

(a)

Find inverse of the following
function:

(2
Mark)


f(x) =

x^{3}

2

x 3


x

3


(b) Explain equivalence relation with example.

(2
Mark)

9
(c) Find Boolean expression for the output of
the following logic (3
Marks)
circuit.
For Dec 2016 2017
ReplyDeleteFor Dec 2016 2017
ReplyDeleteThanks it very useful
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