Download JNTUH MCA 1st Sem R13 2021 July-August 811AA Mathematical Foundations Of Computer Science Question Paper

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Code No: 811AA R13

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

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MCA I Semester Examinations, July/August - 2021

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

Time: 3 Hours Max. Marks: 60

Answer any five questions

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All questions carry equal marks

1. a) Prove by indirect method that (¬Q), P ? Q, P ? R ? R
   b) What are the most common rules of inference? [6+6]
2. Write in the symbolic form and negate the following statements:
   a) Everyone who is rich can support charity.
   

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   b) Some people are not appreciated by everyone.
   c) Everyone should help their friends, or their friends will not help them. [4+4+4]
3. Show that the relation of congruence modulo m has ‘m’ distinct equivalence classes.
4. Let C be a collection of sets which are closed under intersection and union. Verify whether (C, ?, n) is a lattice. [6+6]
5. Define monoid. Give examples.
   

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   State the laws of Boolean algebra. [6+6]
6. How many words of length six over the alphabet {a, b, c, d, e} contain two a’s, three b’s and two c’s.
   Find the number of ways the letters of the word MALAYALAM can be scrambled. [6+6]
7. State and explain pigeon-hole principle and explain its applications in detail. [12]
8. Solve the recurrence relation u_n - 5u_n-1 + 6u_n-2 = n . [12]

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9. What is a spanning tree? What is minimum spanning tree? Explain Prim’s algorithm for finding it with illustration. [12]

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