Mathematical foundation of computer science
HNBGU BCA Previous Question Paper 201617
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Section A


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

If f and g are two mappings form R to R given by:
F(x) = x2+3x+1, g(x) = 2x3
Then obtain formula defining fog and gog.



If a, b are any two elements of a group G, prove that:
(ab)1 = b1a1 
Prove that the four fourth roots of unity form a finite abelian group with respect to multiplication.



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



Solve the difference equations:
9ar6ar1+ar2=0
satisfying the condition a0 =0 and a1 = 2. 
Solve the recurrence relation ar+23ar+1+2ar =0 by the method of generating functions with the initial conditions a0=2 and a1 = 3.


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

Prove that each of the following is a tautology:
 p>(p v q)
 (p ^ (p>q))>q
 p ^ q > p
 p>p

Write the form of the negation of each of the following:
 For all positive integers n, we have n+2>8
 All men are honest or some man is a thief.
 There is at least one person who is happy all the time.
 The sum of any two integers is an even integer.


If G is a finite group and H is a subgroup of G, prove that O (H) is a divisor of O (G).

Find the generators of a cyclic group of order 8.

Read Also:
 Computer Fundamental HNBGU BCA PYQ 2011
 Computer Fundamental HNBGU BCA PYQ 2012
 Computer Fundamental HNBGU BCA PYQ 2013
 Computer Fundamental HNBGU BCA PYQ 2016
 Computer Networks HNBGU BCA PYQ 2018
 Data Structure HNBGU BCA PYQ 2019
 General English HNBGU BCA PYQ 2016
 MFCS HNBGU BCA PYQ 2013
 MFCS HNBGU BCA PYQ 2016
 MFCS HNBGU BCA PYQ 2018
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 Programming in C HNBGU BCA PYQ 2012
 Programming in C HNBGU BCA PYQ 2013
 Programming in C HNBGU BCA PYQ 2016
 Programming in C HNBGU BCA PYQ 2017
 Programming in C HNBGU BCA PYQ 2018