Download JNTUA MCA 2018 July Reg-Supply 1st Sem 9F00104 Mathematical Foundations of Computer Science Question Paper

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MCA I Semester Supplementary Examinations June/July 2018

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

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

Time: 3 hours Max. Marks: 60

Answer any FIVE questions

All questions carry equal marks

1. Verify the identity, inverse and domination laws through truth tables.

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2. Show that P - (Q - P) & ¬P — (P — Q) using (i) truth table. (ii) without truth table.
3. Test whether the following argument is valid:
   I will get grade A in this course or I will not graduate.
   If I do not graduate, I will join the army.
   Therefore, I will not join the army.

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4. Prove the statement “The square of an even integer is an even integer” by the method of contradiction.
5. Explain about the properties of a binary relation in a set with suitable example.
6. Define a partial order relation. Let A be a given finite set and P (A) its power set. Let < be the inclusion relation on the elements of P (A). Draw Hasse diagrams of
   (P(A),?) for (i) A={a,b,c} (ii) A = {a, b, c,d}
7. Write about general properties of an algebraic system.
   

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   With an example, explain the concept of homomorphism and isomorphism.
8. Find the coefficient of x⁶ y⁴ in the expansion of (2x-3y)¹⁰.
9. Explain the principle of inclusion-exclusion with a suitable example.
10. Find a generating function for the recurrence relation a_n+2 - 5a_n+1 +6a_n =2, n=0 and a₀ = 3, a₁ = 7.
11. Prove that the sum of degrees of the regions of a planar graph G is equal to twice the number of edges in G.

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12. What is a spanning tree? Explain any two ways for finding out spanning tree of a given graph with examples.
13. Find the chromatic number of:
    (i) A bipartite graph K_3,5. (ii) A complete graph K_n.
14. What is a Euler circuit? Explain the process of finding a Euler circuit in a given graph.

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