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Reg 1४०:_ Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
THIRD SEMESTER B.TECH DEGREE EXAMINATION(S), MAY 2019
Course Code: (5201
Course Name: DISCRETE COMPUTATIONAL STRUCTURES

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries3 marks. Marks
1 Show that set of all integers are countable. (3)
2 What is the minimum number of students required in a class to be sure that ‏غ3‎ (3)

least six will receive same grade , if there are five possible grades.
With suitable example define GLB and LUB of a partially ordered set. (3)
4 Show that (E,+) E is set of all eve non negative integers is subsemigroup of (N,+) (3)

N is set of all natural numbers.

PART 1
Answer any two full questions, each carries9 marks.
5 9) Solve the recurrence relation an=4ap-1-4an-2+(n+1)2" (5)
b) Let R={(1,2),(3.4),(2,2)} 5ಎ((4,2),(2,5),(3,1),(1,3)) Find RoS,SoR,Ro(SoR) 210 (4)
RoR

6 ஐ Let R be the set of real numbers and 5 is the relation on R defined by (x,y)€S if (5)
(x-y) is divisible by 7. Prove that S is an equivalence relation. Find equivalent
class of S.
b) How many permutations are there for the eight letters a,e,f,g,i,t,;w,.x.How many (4)
start with letter “0 and how many start with letter ‘t’ and end with letter “ഠ്‌.
7 8) Check whether the algebraic structure defined over the set of positive (5)

integers is a semigroup or not?

b) Show that Ax(BNC)=(AxB)N(AxC) (4)
PART C
Answer all questions, each carries3 marks.
8 Prove that inverse element of a group is unique (3)
9 Define algebraic system with two binary operations. (3)
10 Prove that every chain is a distributive lattice (3)
11 Define a Boolean algebra. Give an example (3)

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