8/10/2019 final DS 2009 2010
4/5
BIT1113
P A R T B
Answer FIVE (5) questions only.
Q8 (a) Based on the follo win g relations, assign these pairs (
1 , 1 ) , 1, 2) , 2,1) , 2, 2)
to appropriate relations.
(i) R1 = { (a ,b ) I a ^ b}
(ii) R2 = { (a ,b) | a > b}
(4 marks)
(b) Given the set {1, 2, 3, 4} , decide whether the follow ing
relations is reflexive ,
symmetric
or
transitive.
(i) {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)}
(ii) {(1,1),( 1,2),(2,1 ),(2,2),(3,3 ),(4,4)}
(ii i) {(1,2), (2,3)(3,4)}
(4 marks)
Q9 (a) Write an algorithm to find the ma ximu m value from three
numbers; a, b, c.
(4 marks)
(b) Answ er all the questions based on a graph given in FI G UR
E Q9.
b c 6 d
Find the:
(i) length of the shortest path from a to i .
(ii) length of the shortest path from a to z.
(iii) length of the shortest path from a to z that passe s
through c.
(4 marks)
Q10 Let
A = {L, 2, 3, 4, 5
} a n d B =
{0, 2, 4, 6, 8
}. Suppose
R
is
a
relation from
A
to
which is defined as follows . Write down the elements of
R.
(a) x R y *
x ^ y.
(2 marks)
4
8/10/2019 final DS 2009 2010
5/5
BIT1113
(b) x R y *
x - y is even.
(3 marks)
(c) x Ry x + y = 7.
(3 marks)
QLL (a) Le tA = { l , 3, 5} and
B
= {
S
, t , u, v}. A function f is given in FIG UR E
Q l l be low .
A B
F I G U R E Q l l
(i) Identify the domain and co-dom ain for function f.
{"(a,a) y*(*a,b)',
1
(b , c ' f / i c^d ) ' , ( c f /a ) , ld , b ) }
Q12 (a ) P r ov e that 6 x 7 " - - 2 x 3 " i s d iv is ib le b y
4
(b) Sho w that
+ 2 n
i s 0 ( n
2
)
n + 1
Q13 Solve the follow ing recurrence relation,
a
n
= 8a
n
- - 16a
n
-
2
, where a
0
= 1, a = 2.
(3 marks)
(4 marks)
(4 marks)
(8 marks)
5
