JNTUA MCA 1st Sem last 10 year 2010-2020 Previous Question Papers (JNTU Anantapur)
Code: 9F00104
MCA I Semester Regular & Supplementary February 2014 Examinations
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MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
(For 2009, 2010, 2011, 2012 & 2013 admitted batches only)
Time: 3 hours Max. Marks: 60
Answer any FIVE questions
All questions carry equal marks
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- (a) Obtain PCNF of (P ? R) ? (Q ? P).
(b) State the laws of algebra of propositions. - (a) Check whether the following arguments are valid or not.
No professors are ignored
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Hence, no professors are vain.
(b) What is predicate logic? Explain free and bound variables with example. - (a) Prove that “A relation on a set A is reflexive if and only if the inverse relation R-1 is reflexive”.
(b) What is a lattice? Explain the properties of lattice. - (a) Prove that the intersection of two submonoids of a monoid is a monoid.
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(b) State and explain the four axioms of a group. With an example, explain about a group. - (a) How many integers between 103 and 104
(i) Have no digits other than 2, 5, 8?
(ii) Have no digits other than 0, 2, 5 or 8?
(b) Explain the principle of inclusion-exclusion for n sets. - (a) Solve the recurrence relation an = nan-1 for n > 1, given that a1 = 1.
(b) Write the working procedure for solving non-homogeneous finite order relations. - (a) Prove that the sum of degrees of the regions of a planar graph G is equal to twice the number of edges in G.
(b) Define a graph. Explain various types of graphs with example. - (a) Find the chromatic number of the graph.
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