## [DCS] CS201 DISCRETE COMPUTATIONAL STRUCTURES MODAL QUESTIONS FOR SECOND YEAR S3 APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

PART A

(Answer any 2 questions,2 x 5 = 10 Marks)

1. a) Explain Quantifiers

b) Explain the rules US and EG

2. Show that any proposition e can be transferred into CNF

3. Show that R is a valid inference from the premises P→Q, Q→R and P

4. Form a recurrence relation corresponding to the sequence {4, 12, 36, 108, 324...} and also find its solution.

5. A relation R on the set of all integers Z is defined as

aRb iff  a-b is divisible by m

Show that R is an equivalence relation on Z

PART B

(Answer any 2 questions,2 x 5 = 10 Marks)

1. Show that (R→~ܳQ) , (R V S) ,(S →~Q),(P →Q) ⇒ ~P ܲ are inconsistent using indirect method of proof.

2. Show that the premises “one student in this class knows how to write programs in JAVA “and “Every one who knows how to write programs in JAVA can get a high paying job”
imply the conclusion “Some one in this class can get a high paying job”

3. How many numbers of symmetric or reflexive relations are possible on an n- element set A?

4. Let A be any non-empty set and R be an equivalence relation defined on A. if a,b are in A Show that the following facts.