Reg No.:

Max. Marks: 100

10

11

ಬ

0)

ಬ

0)

ಬ
0)

02000CS201092002 Pages: 2

Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
Third Semester B.Tech Degree (S,FE) Examination December 2020

Course Code: 5201
Course Name: DISCRETE COMPUTATIONAL STRUCTURES

PARTA
Answer all questions, each carries 3 marks.
Draw the Hasse diagram of posets under the partial order relation of divisibility
A={1,2,3,5,6,10,15,30}
Determine whether the relation R={(a,b)|a > 0} on the set of real numbers is an
equivalence relation.
In how many ways can letters in the English alphabet be arranged so that there
are exactly 7 letters between the letters ‘a’ and ‘b’.
Among the first 500 positive integers, determine the integers which are not
divisible by 2, nor by 3, nor by 5.
PART B
Answer any two full questions, each carries 9 marks.
Let f(x)=x+2, g(x)= ೫-2 and h(x)=3x for x € R, where R is the set of real
numbers. Find gof , fog, fof, gog, foh, hog , hoh and fohog
If the function f is defined by f(x) = x 2+ 1 on the set {-2, -1, 0, 1, 2}, find the
range of f.
Show that the set N of natural numbers is a semigroup under the operation
x*y = max(x,y). Is it a monoid?
8 scientists and 5 politicians take part in a conference. In how many ways can
they be seated in asingle rowif (i) no 2 politician must sit together
(11) no 2 scientist must sit together.
Solve the recurrence relation ay = 6 ‏ممع 9 - رمد‎ , 1 > 2 and 2५ = | and 21 = 4

Show that A X (BNC) = (^>) ೧ (൧൧.
PART C
Answer all questions, each carries 3 marks.
Define group homomorphism.

How many proper subgroups will be there for a group of order 11? Justify your
Answer.

Let (L,<) be 8 lattice and a,b,c,d elements of L. Prove that if കടം and bavb
Define a complemented lattice. Give an example.

Page 1 of 2

Duration: 3 Hours

Marks
(3)

(3)

(3)

(3)

(4)

(5)

(4)

(5)

(5)
(4)

(3)
(3)

(3)

(3)