Download JNTUA MCA 2019 May Reg-Supply 1st Sem 9F00104 Mathematical Foundations of Computer Science Question Paper

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Code: 9F00104

MCA I Semester Supplementary Examinations May/June 2019

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

(For 2009, 2010, 2011 & 2012 (LC), 2013, 2014, 2015 & 2016 admitted batches only)

Time: 3 hours Max. Marks: 60

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Answer any FIVE questions

All questions carry equal marks

1. Differentiate between PDNF and PCNF with two examples.
2. State and explain the rules that can generate a well formed formula and give an example.
3. Prove or disprove the validity of the following arguments using the:
   1. Rules of inference,

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   2. All men are fallible,
   3. All kings are men,
   4. Therefore, all kings are fallible.
4. Show that R is valid conclusion from the given set of premises P, P ? Q, Q ? R.

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5. Show that the sets of even numbers and odd numbers are both recursive.
6. Differentiate equivalence relation and partial ordering relation with example.
7. Let G = {—1,0, 1}, verify whether G forms a group under usual addition.
8. If a, b are any two elements of a group (G,.) which commute, show that a^-1 and b commute, b^-1 and commute, a^-1 and b^-1 commute.
9. Show that if eight people are in a room, at least two of them have birthday that occur on the same day of the week.

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10. How many ways are there to place 20 identical balls into 6 different boxes in which exactly 2 boxes are empty?
11. Solve a_n — 5a_n-1 + 6a_n-2 = (n+1)2ⁿ, a₀ =0, a₁ = 1.
12. Solve a_n — 7a_n-1 + 12a_n-2 = 0; n > 2 by generating function.
13. Differentiate between BFS and DFS with an example.
14. In any planar graph, show that |V| — |E| + |R| = 2.

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15. Define Hamiltonian cycles and write basic rules for constructing Hamiltonian cycles.
16. Define chromatic number and explain it with four examples.

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