B B1812 Pages: 2

Reg No.: Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER MCA DEGREE EXAMINATION, JULY 2018

Course Code: RLMCA103
Course Name: DISCRETE MATHEMATICS
Max. Marks: 60 Duration: 3 Hours
PART A
Answer all questions, each carries 3 marks Marks

1 Define antisymmetric relation with an example. (3) 2 Let A={1,2,3,4} and
ಔಎ((1,1),(1,4),(4,1),(4,4),(2,2),(2,3),(3,2),(3,3)]. Write the (3) matrix of R and sketch its graph.

3 State Chinese Remainder theorem. (3)
4 How many arrangements are there of all letters in the word SOCIOLOGICAL? (3)
5 Define Bipartite graph and Complete graph. Can a bipartite graph be complete? (3)
6 Define planar graph. Check whether the graph given below is planar. If yes, draw (3) the

planar embedding.
7 Let p: Triangle ABC is isosceles. Q: Triangle ABC is equilateral. Translate the (3)

statement ~p — ~q into an English sentence.
8 If ‏و ,م‎ are primitive statements, prove that (~pVq)A(pA(pAq))& (paq). (3)

PART B
Answer six questions, one full question from each module and carries 6 marks
Module I

9 Let U={1,2,3,4,5,6,7}, A={1,2,3,4,7}, B={2,3,4,5,6}. Verify DeMorgan’s laws. (6) OR
10 Prove that if f: ಗಿಡಿ and ഉ : BC are both one-one and onto , then gef is also (6) one-

one and onto. Also prove that (हन) 111௨2,

Module 11
11 Write the gcd(12378,3054) as the linear combination of the two numbers. (6) OR
12 Show that 41 divides 229-1 using properties of congruences. (6)
Module III
13 a) A student is to answer 7 out of 10 questions on an examination. In how many (3)
Page 1 of 2

B B1812 Pages: 2

ways can he make his selection if he must answer the first two questions.