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[Fall
2014] ASSIGNMENT
PROGRAM
BSc IT
SEMESTER
SECOND
SUBJECT
CODE & NAME BT0069, Discrete Mathematics
CREDIT 4 BK ID B0953 MAX. MARKS 60
Q. No. 1 A bit is either 0
or 1: a byte is a sequence of 8 bits. Find the number of bytes that, (a)can be
formed (b)begin with 11 and end with 11 (c)begin with 11 and do not end with 11
(d) begin with 11 or end with 11. 4x2.5 10
Answer:
(a)
Since the bits 0 or 1 can
repeat, the eight positions can be filled up either by 0 or 1 in 28
2 (i) State the principle
of inclusion and exclusion.
(ii) How many arrangements
of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 contain at least one of the patterns
289, 234 or 487? 4+6 10
Answer:
I)
Principle of Inclusion and
Exclusion
For any two
sets P and Q, we have;
i) |P ﮟ
Q| ≤ |P| + |Q| where |P| is the number of
elements in P, and |Q| is the number elements
3 If G is a group, then
i) The identity element of
G is unique.
ii) Every element in G has
unique inverse in G.
iii)
|
For any a єG, we have (a-1)-1 = a.
|
iv) For all a, b є G, we have (a.b)-1 = b-1.a-1.4x
2.5 10
Answer: i) Let e, f be two identity
elements in G. Since e is the identity, we have e.f= f.
Since f is the identity, we have e.f = e.
Therefore, e = e.f = f.
Hence the identity element is unique.
4 (i)Define valid argument
(ii) Show that ~(P ^Q)
follows from ~ P ^ ~Q.5+5= 10
Answer: i)
Definition
Any
conclusion, which is arrived at by following the rules is called a valid
conclusion and argument is called a valid argument.
5
(i)Construct a grammar for the language.
|
'L⁼{x/ xє{ ab} the number of as in x is
a multiple of 3.
|
(ii)Find the highest type
number that can be applied to the following productions:
1. S→A0, A → 1 І 2 І B0,
B → 012.
2. S →ASB І b, A → bA І c ,
3.
S → bS І bc.5+5
10
Answer: i)
Let T = {a, b} and N = {S, A, B},
S is a
starting symbol.
6 (i) Define tree with
example
(ii) Any connected graph
with ‘n’ vertices and n -1 edges is a tree. 5+5 10
Answer: i)
Definition
A
connected graph without circuits is called a tree.
Example
Consider the two trees G1 = (V, E1) and
G2 = (V,
E2) where V = {a, b, c, d, e, f, g, h, i, j}
Get fully solved assignment, plz drop a mail with your sub code
computeroperator4@gmail.com
Charges for mba rs 125/subject and rs 700/semester only.
For other rs 125/subject only
if urgent then call us
on 08791490301, 08273413412
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