MFCS Previous Year Question Paper 2016 | HNBGU BCA First semester

Mathematical foundation of computer science

HNBGU BCA Previous Question Paper 2016-17

    1. Define partial order relation. Give an example of a relation which is reflexive but neither symmetric nor transitive.

    2. If f and g are two mappings form R to R given by:
      F(x) = x2+3x+1, g(x) = 2x-3
      Then obtain formula defining fog and gog.

    1. If a, b are any two elements of a group G, prove that:
      (ab)-1 = b-1a-1

    2. Prove that the four fourth roots of unity form a finite abelian group with respect to multiplication.

    1. Determine which of the following are even permutation:
      (i) F= (1,2,3) (1,2)
      (ii) G= (1,2,3,4,5) (1,2,3) (4,5)
      (iii) H =(1,2) (1,3) (1,4) (2,5)

    2. Give an example of a finite abelian group which is not cyclic.

    1. Solve the difference equations:
      satisfying the condition a0 =0 and a1 = 2.

    2. Solve the recurrence relation ar+2-3ar+1+2ar =0 by the method of generating functions with the initial conditions a0=2 and a1 = 3.

  1. If R is additive group of real number and R+ the multiplicator group of positive real number, prove that the mapping f:R->R+ defined by f(x) = ex is an isomorphism

  2. Prove that each of the following is a tautology:

    1. p->(p v q)
    2. (p ^ (p->q))->q
    3. p ^ q -> p
    4. p->p
  3. Write the form of the negation of each of the following:

    1. For all positive integers n, we have n+2>8
    2. All men are honest or some man is a thief.
    3. There is at least one person who is happy all the time.
    4. The sum of any two integers is an even integer.
    1. If G is a finite group and H is a subgroup of G, prove that O (H) is a divisor of O (G).

    2. Find the generators of a cyclic group of order 8.