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Fall- 2012
Bachelor In Information Technology (B.Sc-IT)
Semester - II
Discrete Mathematics 4 Credits BT0069
(Book ID: B0953)
Assignment Set 1 (60 Marks)
Answer All Questions 6 X 10 = 60 Marks
1. Find x and y if(3x+y, x 1) = (x+3, 2y 2x).
2. Suppose a States license plate consist of three letters
followed by
4 digits. How many different plates can be formed if repetitions
are allowed?
3. Find the solution of the recurrence relation an = an 1 + 2an
2 with a0 = 2 and a1 = 7.
4. In a finite Poset S, show that there is always atleast one
maximal element and one
minimal element.
5. Verify whether the set L = {1, 2, 3, 4, 6, 12}, the factors
of 12 under the relationdivisibility forms a lattice.
6. Test whether the set Z (the set of integers), with binary
operation * such that x* y= xy
is a semigroup.
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Fall- 2012
Bachelor In Information Technology (B.SC-IT)
Semester - II
Discrete Mathematics 4 Credits
(Book ID: B0953)
Assignment Set
II (60 Marks)
Answer All Questions 6 X 10 = 60 Marks
1. If there was a meeting then catching the bus was difficult.
If they arrived on time
catching the bus was not difficult. They arrived on time.
Therefore there was no
meeting. Show that the statement constitutes a valid
argument.
2. Give some examples of first order predicates.
3. Test whether D75 is a Boolean Algebra.
4. Generate the language L (G) = , 1n ma ba n m by the
grammar.
, , , , , , ,G S A B C a b S where is the set of
productions.
, , , ,S aS S aB B bC C aC C a
5. Construct the state table for the following DFA.
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6. Define an encoding function,
E:8
2Z 9
2Z
by E(e1 e2 e8) = e1 e2 e9 where,
e9 =
8
i
i 1e
,
the summation being taken under addition modulo 2. If p = 0.001
is the probability that a
signal is received incorrectly, find the probability that the
code word 110101101 is received
with at the most one error.
q q1
Start
state
Final
state
00
0,1
1 1
