B C192006 Pages:3

Reg No.: Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
THIRD SEMESTER B.TECH DEGREE EXAMINATION(R&S), DECEMBER 2019
Course Code: 1
Course Name: DISCRETE COMPUTATIONAL STRUCTURES

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries3 marks. Marks
1 Let f(x) =x+2 g(x) = 5-2 and h(x) = 3x for x IR, where R is the set of real (3)
numbers. Find foh, hog , fo(goh)
2 Let R be a relation on set A .Prove that if R is reflexive then R™ is also (3)
reflexive
3 In how many ways can 12 balloons be distributed at a birthday party among (3)

10 children if we ensure that every child gets atleast one balloon.
4 Show that the set N of natural numbers is a monoid under the operation x* y= (3)

max(x,y).

PART 8
Answer any two full questions, each carries9 marks.
5 ച Prove that (1) ۸٥9ط‎ or (A- 8) ‏تا‎ (8 - A) = (^ UB) - (ANB) (5)
(ii) (A- C) ( -- ¢) = (^ 183) - ९ Where A, B and C are any sets.

b) How many permutations can be made with the letters of the word (4)
MISSISSIPPI taken all together? How many of these will be vowels
occupying the even places?

6 ஐ Let X ={ 2,3,6,12,24,36} and the relation be such that x Give the relation and draw the Hasse diagram of (X, <). Also find the
maximal and minimal elements.

b) Solve the recurrence relation a, + ‏ربج‎ = 3r 2" using characteristic root method (5)
7 8) State Pigeon hole principle. Show that among any 11 numbers there existat (4)

least 2 numbers with the same unit digit.

b) Let A={1,2,3....11,12} and let R be the relation on A x A defined by (a,b) R (5)

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