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B B3B037 Total Pages:3

Reg. No. Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
THIRD SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2017

Course Code: CS 201
Course Name: DISCRETE COMPUTATIONAL STRUCTURES (CS, IT)

Max. Marks: 100 Duration: 3 Hours

PART A
Answer all questions. Each Question carries 3 marks

1. Show that (A-B) — C=A-(B U ©

2. Show that the set of integers of positive, negative and zero are denumerable.

3. Show that if any five integers from | to 8 are chosen, then atleast two of them will
have a sum 9.

4. Define:Partition,antisymmetric, Semigroup homomorphism.

PART B

Answer any two questions. Each Question carries 9 marks.
5. a. Prove that every equivalence relation on a set generates a unique partition of the set
and the blocks of this partition corresponds to R-equivalence classes. (4.5)
b.Let X= (1, 2 ...... 7 tand R= {/X-Y is divisible by 3}. Show that R is an
equivalence relation. Draw the graph R. (4.5)

6. a. In how many ways can the letters of the word MONDAY be arranged? How many of
them begin with M and end with Y?How many of them do not begin with M_ but end
with Y? (4)

0. Solve ‏مبوة‎ — 4 ani) + ‏مو4‎ = 2" , 8051 ௨-1 (5)

7. a. Draw Hasse diagram for 0100. Find GLB and LUB for B={10, 20}B={5,10,20,25 }
(3)
b. Let X= {1,2,3} and f,g,h be function from X 10 X given by f={(1,2) , (2,3) , (3,1))
‏خط })1,2),(2,1),(3,3({ دع‎ { (1,1), (2,2),(3,1) }. Find fog, goh,fohog. (3)
c. Ina class of 25 students, 12 have taken Mathematics, 8 have taken Mathematics but
not Biology. Find the number of students who have taken Mathematics and Biology
and those who have taken Biology but not Mathematics. (3)

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