Programme Code : MCA
Course Code : MCS-013
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Year : 2012 Views: 1324 Submitted By : Monika On 20th September, 2012

Do you have solution for this Question. If yes    I aslo want solution.

Q.


a) Make truth table for followings:

i) ~p→(q

ï

r)

ï

p

ï

~q

ii) ~p→ ~r ï q

ï

~p ï 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) (

ï¤

x) (

ï¢

y) ( ï¢ z) P

ii) ï¤ (x) ( ï¤ y) (

ï¢

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

ï

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 ï  Q) ï  (P ï Q)

ïº

(~P + Q) ï (Q ï  P)

c) If p an q are statements, show whether the statement [(~p→q) ï (q)] → (p ï q)

is a tautology or not.



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

ï

Bï C

iii. A\B

Question 5: Marks (4+4 +2)

a) Draw a Venn diagram to represent followings:

i) (A

ï

B) ï (C ï B)

ii) (AïB)

ï

(B ïC)

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.



b) Find inverse of the following functions

i) f(x) =

353ï­ï­xx

3ï¹x

ii) f(x) =

4723ï­ï­xx

2ï±ï¹x

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 Demorganâs Law? Explain the use of Demorgenâs 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.


No Answer Found