Download JNTUA MCA 2016 May Supply 1st Sem 9F00104 Mathematical Foundations of Computers Science Question Paper

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Code: 9F00104

MCA | Semester Supplementary Examinations May 2016

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

(For students admitted in 2010, 2011, 2012, 2013, 2014 & 2015 only)

Time: 3 hours Max. Marks: 60

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Answer any FIVE questions

All questions carry equal marks

1. What is normal form? Explain applications of normal form using relevant examples.
2. Present the implication of the following formula:
   (A?B)?B ? A?B

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3. Discuss about how predicative logic can be applied in a context.
4. What is proof of contradiction? Write an expression to prove contradiction.
5. Draw the Hasse diagram for relation R on I = {1, 2, 3, 4, 5}, whose relation matrix is given below.

    1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 

6. Define Subgroups homomorphism. State an example to explain the concept.
7. How many ways can 3 integers be selected from a set of integers 1, 2, 3, 4, .... 30? So that their sum is even.

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8. State and explain the following:
   • Binomial multinomial theorem.
   • Pigeon hole principle.
9. Using generating function. Solve Y_n+2 —4Y_n+1+ 3Y_n =0 given Y₀=2, Y₁ = 4.
10. Solve the recurrence relation by using substitution method:
    

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    t_n = t_n-1 + n, where t₁=2
11. Explain how minimal spanning tree of an undirected weighted graph G can be constructed using Prim's algorithm.
12. Write short notes on the following:
    • Isomorphism and sub-graphs.
    • Euler circuits.
    • Hamiltonian graphs.

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