MFCS previous year question paper 2021 | HNBGU MCA first semester

Admin - January 19, 2024

MFCS

HNBGU MCA Previous Question Paper 2021-22

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    UNIT I

    1. Define equivalence relation. Define a relation R on the set of Human being as "is brother of". Is the relation R equivalence relation? justify your answer.

    2. Consider the funciton

      F,g:A->A defined by:
f(x) = x^2+3*x+1
g(x) = 2*x-3
Find the composition functions:
(i) fog (ii) gof

    1. Consider a relation defined on the set A = {a,b,c,d} as R={(a,b),(b,c),(c,d),(b,a)}. Find the transitive closure of R.

    2. Consider the realtion R defined on a set of integers as R = {(a,b)E ZxZ} such that a<b. Find the reflexive and symmetric closure of R.

    3. UNIT II

    1. Write the principle disjunctive normal form of teh formula P->R.

    2. Show that {|^} is functionally complete set of connective.

    1. Prove that the statement formula (P->Q) <-> (!Q->!P) is a tautology. How is a tautology. How is tautology related with equivalence of formulas? Explain with example.

    2. Show by means of an example that the negation of a formula is equivalent ot its dual with negative variables.

    5. UNIT III

  5. Draw Hasse diagram of he relation defined on A= {a,b,c,d,e} whose relation matrix is : 

    Mr = 10111
01111
00111
00010
00001

  6. Solve the recurrance relation:

    Fn=5Fn-1-6fn-2
with f0=1 and f1-4.
    7. UNIT IV

    1. Write generation function corresponding to the follwing sequences: 

      (i) <1,1,1,1,1,.....>
(ii) <1,a,a^2,a^3,....>

    2. Using principle of mathematical induction, prove that: 

      1+3+5+...+(2n-1)=n^2
for n=1,2,3

  8. Write short notes of any two of the following:

    1. Asymptotic behaviour of function
    2. Posets
    3. Warshall's algorithm
    4. Abelian group

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