Old Exam Papers June 2012 (Set 2)

(b) Find D.N.F. of the following :
b1 2 3g 1 c2 3h
'
f x , x , x x . x . x '
fuEu dk fo;ksth izlkekU; :i Kkr dhft;s %
b1 2 3g 1 c2 3h
'
f x , x , x x . x . x '
6. (a) Let a and b be two numeric functions such that :
a
and b
r
r
R
S
T
1, 0 r 2
0, 0 3
R
S
T
2, 0 r 3
3, r 4
then find convolution c a* b .
ekuk a ,oa b nks la[;kad Qyu bl izdkj gaS fd %
a
vkSj b
r
r
R
S
T
1, 0 r 2
0, 0 3
R
S
T
2, 0 r 3
3, r 4
rc Kkr dhft;s dUoksywlu c a* b .
600 6 MT-01
rc FSA, A n , S, Y , s0 , fs
ds fy, laØe.k vkjs[k
Kkr dhft;sA
5. (a) Let B l1 , 5, 7, 35q
and binary operations + and .,
unary operation ' defined on B, such that , a, b B,
b g
a b l.c.m. a, b
a.b g. c. d. ba , bg
a'
a
35
then show that bB, ,
.,'g
is Boolean Algebra.
ekuk B l1 , 5, 7, 35q
ij f}vk/kkjh lafØ;k,¡ +, . ,oa
,dvk/kkjh lafØ;k * fuEu izdkj ifjHkkf"kr gS % izR;sd
a,b B ds fy,
a b a, b dk y?kqÙke lekiorZd
a.b a, b dk egÙke lekiorZd
a'
a
35
fl) dhft;s fd bB, ,
.,'g
cwyh; chtxf.kr gSA
MT-01 5 PTO