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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER REGULAR MCA DEGREE EXAMINATION, JULY 2017

RLMCA 103: DISCRETE MATHEMATICS
Max Marks: 60 Duration:3 Hours
PARTA
Answer All Questions. Each question carries 3 marks.
1. Show that (AUB)*=A‘DOB‘
2. Find GCD(256,18)
3. Find the number of arrangements of letters of the word MISSISSIPPI in which the 4
I’s come together.
4. Find awhena = 58 witha=2.
5. Define Regular graph and Connected graph with example.
6. A connected planar graph has 9 vertices having degrees 2,2,2,3,3,3,4,4,5.How many
edges are there? How many regions are there?
7. Define Tautology and show that (றப) © ‏م‎ 15 a tautology.
8. Show that p®q and Opvgq are logically equivalent.
PART ந
Answer All Questions. Each question carries 6 marks.

MODULE I
9. Define equivalence relation. Prove that for x, y € Z the relation defined by R=

{(x,y):5 divides x—-y} is an equivalence relation.

OR
10. Let f: R-{3} © R-{1} defined by f(x)=— .Check whether f is bijective? Find the
inverse if any.
MODULE II
11. Solve the linear Diophantine equation 172x + 20y = 1000.
OR

12. Solve the set of simultaneous congruences x02(mod3) , x03(mod5), x02(mod7)
MODULE III
13. A committee of 10 people is to formed from 12 men and 8 women. In how many ways

can the committee be formed if

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