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C1B002 Total Pages:3

PART 8
Answer All Questions. Each question carries 6 marks

MODULE 1

Let U={1,2,3,4,5,6,7,8,9,10}, A={2,4,6,8}, B={1,3,5,7},c={1,4,8,10}. Verify
Demorgan’s laws.

OR

Write warshall’s algorithm. Use it to find the the transitive closure of the relation.
((1,3), (3,2), (2,4), (3,1),(4,1) on (1,2,3,4)}

MODULE 2
Write GCD of 858 and 325 as a linear combination of thetwo numbers.
OR

Solve the set of simultaneous congruence.x = 2(mod 3) ; x = 3(mod 5); x =
3(mod 7)

MODULE 3

Students are awarded for grades A, B, C & D. How many students must be there in a

group, so that at least 6 students get the same grade?
a. b) How many positive integers not exceeding 100 are divisible by 4 or 6.

OR

How many integers between 100 and 999 inclusive a) are not divisible by 4 b) are
divisible by 3 or 4 c) are divisible by 3 but not by 4.
MODULE 4
Solve the recurrence relation.2 ஐ, = 7 वा1-1 - 3௨2: = 2,a, > 5
OR

Solve the recurrence 10181000 2 — 8 മം + 16a, = 8(5") + 6(4"):n=
Oand ‏يه, 12 = مه‎ = 5

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