August 2010

Subject Code : MC0063 Assignment No: 01

Subject Name: Discrete Mathematics

Marks: 60

Credits : 4 Bk Id B0676 and B0677

Answer the following: Each question carries 10 Marks.

1. If }65/{ 2 xxxA , B = {2, 4}, C = {4, 5} find

(i) )()( CBBA

(ii) )()( BCAB

(iii) )( BAA

2. Using mathematical induction prove that

6

)12)(1(.....321 2222

nnn

n

3. Prove that the number of partitions of n in which no integer occurs more than

twice as a part is equal to the number of partitions of n into parts not divisible by

3.

4. Prove that if S contains more than two elements, then there exist f, gA(S),

such that

fggf

5. Prove that )(modmba and )(modnba if and only if

)),((mod nmlcmba

6. Construct a grammar for the language

}3',},{/{ ofmultipleaisxinsaofnumberthebaxxL

August 2010

Subject Code : MC0063 Assignment No: 02

Subject Name: Discrete Mathematics

Marks: 60

Credits : 4 Bk Id B0676 and B0677

Answer the following: Each question carries 10 Marks.

1. Determine the number of integers between 1 to 250 that are divisible by any of

the integers 2, 3, 5 and 7.

2. Solve the recurrence relation 2,2 21 naaa nnn , given a0 = 3, a1 = – 2

using the generating function.

3. Prove that “If L is a distributive lattice, then it is a modular lattice”

4. Prove that for any a and b in a Boolean algebra,

(i) baba (ii) baba

5. Explain the concept turing machine with example.

6. The generator matrix for an encoding function 6

2

3

2: ZZE is given by

101100

110010

011001

G