Reg No.:

Max. Marks: 100

2

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5 ஐ
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00000CS201121901

Pages: 3

Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Third Semester B.Tech Degree (S,FE) Examination January 2022 (2015 Scheme)

Course Code: 5201
Course Name: DISCRETE COMPUTATIONAL STRUCTURES

PARTA
Answer all questions, each carries 3 marks.
Let X={1,2,3,4} and R={|x>y}. Draw the graph of R and give its matrix.
Assume A = {1,2,3} and p(A) be its power set. Let ೧ be the subset relation on
power set. Draw the Hasse diagram of (p(A), S).
Prove that if any 30 people are selected, then we may choose a subset of 5 so
that all 5 were born on the same day of the week.
In how many ways can we arrange “FUZZTONE?” so that all vowels come
together?
PART छ
Answer any two full questions, each carries 9 marks.
Let f(x)=x+2, g(x)=x-2, h(x)=3x, for x ൦൯. the set of real numbers. Find gof,
fog,fof, ए), hog, hof and fohog.
Consider a set of integers from | to 250. Find
a) How many of these numbers are divisible by 3 or 5 or 7
b) How many are divisible by 3 or 7 but not 5.
c) Number of integers divisible by 3 or 5.
Solve the recurrence relation a, “പേ 7 3-2 7 ஷே With 20 = 5, a; = —9, and
22 = 15.
Draw the Hasse diagram for divisibility on the set {1, 2, 3, 4, 5, 6, 7, 8}.
Prove that the set of Idempotent elements of a commutative monoid{M,*,e}
forms a submonoid of M.
Show that a mapping f:R->R be defined by f(x)=ax+b, where ೩,0,೫ € 1२, a0 15

invertible. Define its inverse.

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Duration: 3 Hours

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