MFCS previous year question paper 2021 | HNBGU MCA first semester


HNBGU MCA Previous Question Paper 2021-22

    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.

    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.

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

    Mr = 10111
  2. Solve the recurrance relation:

    with f0=1 and f1-4.
    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:

      for n=1,2,3
  3. Write short notes of any two of the following:

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