BT0069, Discrete Mathematics

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Spring 2015  ASSIGNMENT
PROGRAM
BSc IT
SEMESTER
SECOND
SUBJECT CODE & NAME
BT0069, Discrete Mathematics
CREDIT
4
BK ID
B0953
MAX.MARKS
60

Q.1 If U = {a,b,c,d,e}, A ={a,c,d}, B = {d,e}, C = {b,c,e}
Evaluate the following:
(a) A’ ´ (B-C)
(b)(AÈB)’´(BÇC)
(c)(A-B)´(B-C)
(d)(BÈC)’´A
(e)(B-A)´C’

Answer:
(a) A’ ´ (B-C)
A’ = set of those elements which belong to U but not to A.
A’ = (b, e)
(B-C) = (d)
 A’ ´ (B-C) = (b,e)´(d)







2 (i) State the principle of inclusion and exclusion.

Answer:
I)                    Principle of Inclusion and Exclusion
For any two sets P and Q, we have;
i) |P Q| ≤ |P| + |Q| where |P| is the number of elements in P, and |Q| is the number elements in Q.


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 ebe two identity elements in G. Since is the identity, we have e.ff. Since is the identity, we have e.e. Therefore, e.f. Hence the identity element is unique.
ii)Let be in and a1, a2


4 (i) Define valid argument
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.

Answer: i)
Let T = {a, b} and N = {S, A, B},
is a starting symbol.
The set of productions: F
S
®
bS
S
®
b
S
®
aA


6 (i) Define tree with example
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}
E1 = {{a, c}, {b, c}, {c, d}, {c, e}, {e, g}, {f, g}, {g, i}, {h, i}, {i, j}} E2 = {(c, a), (c, b), (c, d), (c, f), (f, e), (f, i), (g, d), (h, e), (j, g)}
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Send your semester & Specialization name to our mail id :
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