Guru Gobind Singh Indraprastha Vishwavidyalaya 2007 B.C.A Computer Application Mathematc-II - Question Paper
Tuesday, 28 May 2013 03:20Web
Q1 (a) A set is called odd (respectively, even) set if the number of elements in it
us odd (respectively, even).
(i) How many odd sets of {1,2,3………n) are there? (1.5)
(ii) How many even sets of {1,2,3……...n) are there? (1.5)
(b) calculate the transitive closure of R={(1,2),(2,3),(3,4),(4,5)} on {1,2,3,4,5}. (3)
(c) provide an example of a 2 variable fucnction which is continuouis at (1,1) but is
not differentiable there. (3)
(d) Test whether f(x)=x2+1 from the set of positive real number to the set of positive
Real number is (i) one-one, (ii) onto. (3)
(e) Check whether (P (S) ) is a lattice, where S is a finite set and P(S) is the poer set
or S. (3)
(f) State Euler’s Theorem. (3)
(g) obtain the shortest distance from the point (2,4,1) to the plane 3x+2y+5z=7. (3)
(h) Evalute the double integral f f ex2 dxdy, where the region R is provided by
R:2Y x 2 and 0 y 1. (4)
part - A
Q2 Prove that every partition of a finite set A fives rise to a unique equivalence relation R on
A provide rise to a unique partition of A. (12.5)
Q3 (a) Suppose A C = B C. Does it follow that A =B? justify your ans. (6.5)
(c) Let R={(1,1), (2,2), (3,3) (4,4), (1,2), (2,4), (2,3)} be relation on {1,2,3,4,5,6}.
calculate the
(i) Transitive closure of R
(ii) Largest relation R one such that R1 <= R and R1 is antisymmetric.
(iii) Largest relation R1 such that R1 <=R and R1 is irreflexive. (6)
SECTION- B
Q4 (a) Prove that every non-empty POSET (S, ) has a minimal element. (6)
(b) Prove that for every POSET (S, ), there is a total ordering of S which is
Compatible to the partial ordering . (6.5)
Q5 For every of the subsequent posets, draw the Hasse diagram and determine all maximal
and minimal elements and greatest and lowest elements if they exit. Sepecify which posets
are latties? (12.5)
(a) [D20;|], where Dn is the set of all positive divisors of n and | denotes divides.
(b) [D30;|]
(c) [A;], where A={X| X is a real number and 0
| Earning: Approval pending. |
