MFCS Previous Year Question Paper 2013 | HNBGU BCA First semester

Mathematical foundation of Computer science

HNBGU BCA Previous Question Paper 2013-14

    1. If Q be the set of rational numbers and a function f:Q->Q be defined by f(x) = 2x+3, show that f is bijective. Find a formula that defines the inverse function.

    2. Define a relation and a function. Give and example of a relation which is reflexive and transitive but not symmetric.

    1. Show that the set N of all natural numbers is not a group with respect to addition.

    2. Show that the set of all n, nth roots of unity forms a finite abelian group of order n with respect to multiplication

    1. Decompose the following permutation into transposition:

      1. 1 2 3 4 5 6 7
        6 5 2 4 3 1 7
      2. 1 2 3 4 5 6 7 8
        3 1 4 7 2 5 8 6
    2. If a group G has four elements, show that it must be abelian.

    1. Five the two numeric functions and such that neither asymptotically dominates nor asymptotically dominates

    2. Solve the recurrence relation ar-3ar-1+2ar-2=6, satisfying the initial conditions a0=1 and a1=4.

    1. Solve the difference equation:

      ar+2-2ar+1+ar=3r +5

    2. If f is a homeomorphism of a group G into a group G’ with kernel K, then K is a normal subgroup of G.

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

      1. [(p->q)^(q->r)]->(p->r)
      2. [p^(p->q)]->q
  1. Write the form of the negation of each of the following:

    1. The corresponding sides of two triangles are equal if and only if the triangles are congruent.
    2. If the number x is less than 10, then there is a number y such that x2+y2-100 is positive
    1. If X be the set of factors of 12 and if ≤ be the relation divides, i.e., x ≤ y if and only if x | y. Draw the Hasse Diagram of (X,≤)

    2. Prove that any right (left ) cosets of a subgroup are either disjoint or identical