MFCS
HNBGU MCA Previous Question Paper 202122
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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.

Consider the funciton
F,g:A>A defined by: f(x) = x^2+3*x+1 g(x) = 2*x3 Find the composition functions: (i) fog (ii) gof



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.

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.



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

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



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.

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


Draw Hasse diagram of he relation defined on A= {a,b,c,d,e} whose relation matrix is :
Mr = 10111 01111 00111 00010 00001

Solve the recurrance relation:
Fn=5Fn16fn2 with f0=1 and f14.


Write generation function corresponding to the follwing sequences:
(i) <1,1,1,1,1,.....> (ii) <1,a,a^2,a^3,....>

Using principle of mathematical induction, prove that:
1+3+5+...+(2n1)=n^2 for n=1,2,3


Write short notes of any two of the following:
 Asymptotic behaviour of function
 Posets
 Warshall's algorithm
 Abelian group
UNIT I
UNIT II
UNIT III
UNIT IV