This download link is referred from the post: JNTUH MCA 1st Sem Last 10 Years 2023-2013 Question Papers R20-R09 || Jawaharlal nehru technological university
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Code No: 841AA R17
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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
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MCA I Semester Examinations, October/ November - 2020
MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
Time: 2 Hours Max.Marks:75
Answer any five questions
All questions carry equal marks
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- a) Give the formal definition of a well-formed formula in predicate calculus with examples of formulae that are well-formed and not-well-formed.
b) Show that B is tautologically implied by (—(Av B)—>C)A—AA—C using automatic theorem proving. [7+8] - a) Show that (av —b) A(—av—cvb)A(av—a)is not a tautology.
b) Find a CNF for(p —r) <> (—r —>—p). [7+8] - a) Let R be the following equivalence relation on the set A = {1,2,3,4,5,6} .
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R={(1,1),(1,5),(2,2),(2,3),(2,6),(3,2),(3,3),(3,6),(4,4),(5,1),(5,5),(6,2),(6,3),(6,6) }
Find the partition of A induced by R .
b) Define the following properties of binary relations with examples.
I) Reflexive
II) Symmetric--- Content provided by FirstRanker.com ---
III) Anti symmetric
IV) Transitive. [7+8] - a) Find all group homomorphisms from Z3 into Z6.
b) Define the following terms with examples:
I) Semigroup--- Content provided by FirstRanker.com ---
II) Monoid
III) Group
IV) Abelian group. [7+8] - a) Using the digits 1,2,3 and 5, how many 4 digit numbers can be formed if
I) The first digit must be 1 and repetition of the digits is allowed?--- Content provided by FirstRanker.com ---
II) The first digit must be 1 and repetition of the digits is not allowed?
III) The number must be divisible by 2 and repetition is allowed?
IV) The number must be divisible by 2 and repetition is not allowed?
b) How many different arrangements of the word ELLIPSE are possible if
I) There are no restrictions?--- Content provided by FirstRanker.com ---
II) The arrangement starts with S?
III) Both L’s are together?
IV) The letters are in alphabetical order? [7+8] - a) Determine the values of n and r in the following expressions.
I) nCr =3xnCr+1--- Content provided by FirstRanker.com ---
b) Obtain the coefficient of x4y5z6in (2x2 +y—2z3)15 using multinomial theorem. [7+8] - a) Use generating functions to solve the following recurrence relation:
an=5an-1 —6an-2 for n≥2, a0=0 and a1 =3. [15] - a) Determine whether the graphs shown in the following figure are isomorphic.
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Find the chromatic number of the given graph. [7+8]
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This download link is referred from the post: JNTUH MCA 1st Sem Last 10 Years 2023-2013 Question Papers R20-R09 || Jawaharlal nehru technological university
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