8 Problems in Exam on Discrete Structures | CMSC 250, Exams of Discrete Structures and Graph Theory

Download 8 Problems in Exam on Discrete Structures | CMSC 250 and more Exams Discrete Structures and Graph Theory in PDF only on Docsity! 
    "! $#&%('   ") *,+ ! '  +-/.02143  !
56
! 7* 58 9;:=<29 >@?BA CEDFHG IJ> KML/NPORQTS5FUWVWXZY[O \^]_>@?`V2>BA@A> a -b*, c
dedH
! 3^f  -b3 d,hg *,i dej + ! k ml
nlo - l -+qpr*e  st#vu j +w ! h yx ^-
tl
nlo -"z{-
*e3 mj +wR-5k
!
! |- "}   3^
i de
! ~l
nlo -/€ j +w   3^ l   j +wR- !
5 + !
! ‚k
! rƒ„* !E
!…jEl
nlo - j +w‚- ")y *,p  s†.‡k 5!   i  -ˆ+u l +w* ! 3 l +w33*,i d, u‰+- "
) k }   3*,+ ! *e3$* ! * )h
  c* ! 3 } 
-  i -
)b~ 3B۠k  ^+
dŠ!   i  -H+u l +w* ! 3‹+ ! k ˆyxr
 *e3WŒ"nŽrz
! j +wcf‡* ded k
p WyxR
)  d,j Œns[kR+wR-3^+ ) + 5lde   k *3 yxR
 s’‘“+w 
qj! +B 3 W)h
de)  de
^+-3hz… yx ^io+…+ ~ 3B+-
!”j +k  -
*e 3$ R-* !Rg k *e3 yxR
 s Œns2•–Œ" l! 3hs —‡03b3 5 k  - `
- 2˜ Œ63 "! 3@* !™
)hde
3b3 š5
-  io+ j 3
! ›Œ"œ
- 6g *e- d 3hs 0 ! 3^f  -Bk  u+ ded +qf‡* ! g2}   3^*,+ ! 3
io+wRk +w3  3^ "! 3hs{‘“+wc R+ ! +Hk
p  ^+5 R+2k /
-b*ek 5 * ) ziR j +w +[k
p  ^+ g  "
) k
! 3^f  -B* ! ^+
u‰+-  k
H* !)hd   3’u
) ^+-b*
d 3
! ž8+- yxrl + !R"! 3 ‡ ŸH 3 -  ^+ )hd,"
- dej d
i "do"
) k+u j +wR-
! 3^f  -3hs 
s‡ +qf †
!”j *–¡  - "!  d * !  3+u¢k ˆ˜ Œˆ3 "! 3 )h
! i W
5 5"
! * ! g +-b  -H+u3^ "! 3B* !m
3b* !Rgwd, -b+qf ^£ i¢s@ +qf 
!…j *–¡  - "! ‡ 5" i  -@ "
 3 )h
! i 6
8£ ) s‡ +qf 
!…j *–¡  - "!  " i  -‡ "
 3 )h
! i `
 *,u
ded k [5" i  -3@+u’k   "
¤  3^i  k  3
56g"!  - £ s@ +qf 
!…j *–¡  - "! ‡ 5" i  -@ "
 3 )h
! i 6
 *,uk  - `  3^$i `˜ +-/œ g *,- d 3B+ ! k   "
£  s‡ +qf 
!…j *–¡  - "! ‡ 5" i  -@ "
 3 )h
! i 6
 *,uk  - `)h
!! +@i 6
!”j io+ j 3@+ ! k   "
£ ¥¥¥¥ .@k*e3
- "
*e3Bu‰+- g -
* !Rg5l R- l +w3  3 ‰l +w* ! 3 d +w3 lT - l
ng8 ƒ‹%/+ ! +$f‡-b*,  i "d +qf¦k*e3 d * !  ¥¥¥¥ Œ ˜ œ §  ¨ © š .+
d Œ ˜ s2•–Œ ˜™l! 3"s —# !E
™)y -b
* ! 3 ) k +…+ d f‡*ek ŒhŽŽ3^ "! 3hz "
) k3^ "! ˆ*e3 "! -+ ded, _* !_
 d,"
3/+ !  +u
! gwd *e3k 
B z /*e3^^+- j‚    z+-
k "
* ) 3    sW*,p "! k  u+ ded +qf‡* ! g

r    P   ‚    nŽ     ‚   Z     ¦˜    ‚ 0 ! 3^f  - "
) k+uk  u‰+ ded +8f‡* !Rg5}   3^*,+ ! 3 
s‡ +qf 
!…j 3 "! 3
-  
n~ * !Rg‡
ded +uk ) +w -b3  3 
‹!Rgwd *e3k¢z" *e3^+- j/
! 
k "
* ) 3 ^£ i¢s@ +qf 
!…j 3 "! 3
-  
n~ * !Rg 
k "
* ) 3"z8i 
- “! +¢
n~ * !Rg
‹!Rgwd *e3k ! +- *e3^+- jR£  R’k  3b* !Rgwd,@!   i  -
! 3^f  -H* ! k  3 l
)y@l -+8p*  zwi ’u+-
!…jPl
-*
d) -  *,hz j +w  3^“3kR+8f j +wR- fH+- ~ i "d +qf¦k*e3Bio+ x s .+- ")y *ep {
-*
d -  *,Bu+-
! * ! ) +-b- ") 
! 3^f  -
io+qp  z j +w   3^  
0!  ‘ d
i "doj +w -@f‹+- ~ s ˜ s2• ˜ Ž l! 3hs —
/3  * !  ) *,+ ! + !  ^+ l -+8p  k
Hk  u+ ded +qf‡* ! g *e3“^-  s   * !   ‘“+w 
"j 3  k  u
)  l -+8p "!* !™)hde
33
! * ! k  io++ ~ k
‡k  3  +uk  -b3^t* !  hg -b3hzŠŒ  ˜  œ     Šz "} 
d 3   $ s    $  $  Œ    $      Œ ! ˜   ¨s2• ˜ Ž l! 3hs — Š 
i 6
3  ‡f‡*,k›ŒhŽ *e3^* ! ) $* !  hg -b3* ! *,@3 ) k™k  *–¡  - "! )y i  „f h"! k  3 
dede 3^
! k Pd
- g 3^W* !  hg -6* ! t*e3 ˜ Žrs  -b+qp  k
Wk  - 5  3^/i [
 d,"
3^/„fH+7 *e3^* ! )  l
*,-3‡+u "d,"5"! 3W+u k
‡k
p  k  3
5 3  s ŸH 3 -  ^+  
0!  ‘(R  a j +wR-@fH+- ~ s ¨ ©…s2• ˜  l! 3hs —W*,p "! k  u+ dd +qf‡* !Rg u
) 3  $ ¦˜     

!      §  "$  œ  "   "   -+qp  k
       ˜R   Œ  s ©