• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EDT 00:01
CEST 06:01
KST 13:01
  • Home
  • Forum
  • Calendar
  • Streams
  • Liquipedia
  • Features
  • Store
  • EPT
  • TL+
  • StarCraft 2
  • Brood War
  • Smash
  • Heroes
  • Counter-Strike
  • Overwatch
  • Liquibet
  • Fantasy StarCraft
  • TLPD
  • StarCraft 2
  • Brood War
  • Blogs
Forum Sidebar
Events/Features
News
Featured News
Code S RO8 Preview: herO, Zoun, Bunny, Classic3Code S RO8 Preview: Rogue, GuMiho, Solar, Maru3BGE Stara Zagora 2025: Info & Preview27Code S RO12 Preview: GuMiho, Bunny, SHIN, ByuN3The Memories We Share - Facing the Final(?) GSL47
Community News
BGE Stara Zagora 2025 - Replay Pack2Weekly Cups (June 2-8): herO doubles down1[BSL20] ProLeague: Bracket Stage & Dates9GSL Ro4 and Finals moved to Sunday June 15th13Weekly Cups (May 27-June 1): ByuN goes back-to-back0
StarCraft 2
General
Jim claims he and Firefly were involved in match-fixing Code S RO8 Preview: herO, Zoun, Bunny, Classic The SCII GOAT: A statistical Evaluation DreamHack Dallas 2025 - Official Replay Pack BGE Stara Zagora 2025 - Replay Pack
Tourneys
[GSL 2025] Code S:Season 2 - RO8 - Group A RSL: Revival, a new crowdfunded tournament series SOOPer7s Showmatches 2025 Sparkling Tuna Cup - Weekly Open Tournament Sea Duckling Open (Global, Bronze-Diamond)
Strategy
[G] Darkgrid Layout Simple Questions Simple Answers [G] PvT Cheese: 13 Gate Proxy Robo
Custom Maps
[UMS] Zillion Zerglings
External Content
Mutation # 477 Slow and Steady Mutation # 476 Charnel House Mutation # 475 Hard Target Mutation # 474 Futile Resistance
Brood War
General
BW General Discussion BGH auto balance -> http://bghmmr.eu/ FlaSh Witnesses SCV Pull Off the Impossible vs Shu StarCraft & BroodWar Campaign Speedrun Quest Will foreigners ever be able to challenge Koreans?
Tourneys
NA Team League 6/8/2025 [ASL19] Grand Finals [BSL20] GosuLeague RO16 - Tue & Wed 20:00+CET [Megathread] Daily Proleagues
Strategy
I am doing this better than progamers do. [G] How to get started on ladder as a new Z player
Other Games
General Games
Nintendo Switch Thread Stormgate/Frost Giant Megathread Beyond All Reason Path of Exile What do you want from future RTS games?
Dota 2
Official 'what is Dota anymore' discussion
League of Legends
Heroes of the Storm
Simple Questions, Simple Answers Heroes of the Storm 2.0
Hearthstone
Heroes of StarCraft mini-set
TL Mafia
TL Mafia Community Thread Vanilla Mini Mafia
Community
General
US Politics Mega-thread Things Aren’t Peaceful in Palestine UK Politics Mega-thread Russo-Ukrainian War Thread Vape Nation Thread
Fan Clubs
Maru Fan Club Serral Fan Club
Media & Entertainment
Korean Music Discussion [Manga] One Piece
Sports
2024 - 2025 Football Thread Formula 1 Discussion NHL Playoffs 2024
World Cup 2022
Tech Support
Computer Build, Upgrade & Buying Resource Thread
TL Community
The Automated Ban List
Blogs
A Better Routine For Progame…
TrAiDoS
StarCraft improvement
iopq
Heero Yuy & the Tax…
KrillinFromwales
I was completely wrong ab…
jameswatts
Need Your Help/Advice
Glider
Trip to the Zoo
micronesia
Customize Sidebar...

Website Feedback

Closed Threads



Active: 28739 users

[H] Brainteaser

Blogs > Track
Post a Reply
1 2 Next All
Track
Profile Blog Joined May 2006
United States217 Posts
March 26 2009 16:39 GMT
#1
If any of you have taken a logic course, I'd ask you to give me a hand with this. I'll copy it verbatim.

Finding a Formula(a WFF) given its Truth Table.

Suppose I tell you the distribution of T's and F's under the main operator of a well formed formula; can you find a formula having that as its truth table? For example, suppose we consider a wff with three variables, p, q, and r, and I give you the following column under its main operator as: F, F, T, F, F, T, F, T. Now, find a wff compatible with this column.

Do you think that cleverness and ingenuity are required? Well, it so happens that there is a ridiculously simple mechanical method that solves all problems of this type! Once you realize the method, then regardless of the distribution of T's and F's in the main operator column, you can instantly write down the required formula.

Any help is appreciated!

Strength does not come from physical capacity. It comes from an indomitable will.
micronesia
Profile Blog Joined July 2006
United States24648 Posts
March 26 2009 16:42 GMT
#2
Why
do
you
want
us
to
do
this?
ModeratorThere are animal crackers for people and there are people crackers for animals.
Track
Profile Blog Joined May 2006
United States217 Posts
March 26 2009 16:43 GMT
#3
It's a little assignment for my propositional calculus-based logic course.
Strength does not come from physical capacity. It comes from an indomitable will.
KarlSberg~
Profile Blog Joined September 2003
731 Posts
March 26 2009 16:49 GMT
#4
That does tease my brain, but I'm not to sure I understand the formulation.

F, F, T, F, F, T, F, T
are the evaluation of the formula for
pqr - pq/r - p/qr - p/q/r - /pqr - /pq/r - /p/qr - /p/q/r

Is that it or am I wrong?
There are 01 kind of people who know binary. Those who understand little endian and those who don t.
Track
Profile Blog Joined May 2006
United States217 Posts
March 26 2009 16:52 GMT
#5
I'm not entirely sure where you're going with that. Keep in mind the truth table takes into account every possible combination for the three variables. Also let it be noted that the "column under the main operator" speaks to the validity of the entire formula.

For example, if the equation was (p^q)-->r (p AND q) implies r

then if p^q is true and r is false, the validity of the formula would be an F. However, is p^q is true and r is true, or any other combination than the aforementioned, the validity of the formula, or the "column under the main operator" would be listed as T(for valid).
Strength does not come from physical capacity. It comes from an indomitable will.
StRyKeR
Profile Blog Joined January 2006
United States1739 Posts
March 26 2009 16:52 GMT
#6
guess if you can find the algorithm with this hint

Assuming that this is the distribution

p q r | value
F F F | F
F F T | F
F T F | T
F T T | F
T F F | F
T F T | T
T T F | F
T T T | T

f(p, q, r) = (F and T and F) or (T and F and T) or (T and T and T)
Ars longa, vita brevis, principia aeturna.
KarlSberg~
Profile Blog Joined September 2003
731 Posts
March 26 2009 16:58 GMT
#7
On March 27 2009 01:52 StRyKeR wrote:
guess if you can find the algorithm with this hint

Assuming that this is the distribution

p q r | value
F F F | F
F F T | F
F T F | T
F T T | F
T F F | F
T F T | T
T T F | F
T T T | T

f(p, q, r) = (F and T and F) or (T and F and T) or (T and T and T)

That's what I thought too yes. Finding a WFF is just that easy, even though it can be ugly.
Finding an elegant and short one could indeed require more ingenuity. But not that much.
There are 01 kind of people who know binary. Those who understand little endian and those who don t.
Khenra
Profile Blog Joined January 2009
Netherlands885 Posts
Last Edited: 2009-03-26 17:22:26
March 26 2009 17:08 GMT
#8
I came up with the following formula that fits:

(p --> r) AND ( NOT(p) --> NOT(q --> r))

which translates to:

(NOT(p) OR r) AND (p OR q) AND (p OR NOT(r))

Have no idea about an algorithm yet tho

Edit: I guess the people that posted above have the algorithm sorted Just make an AND-structure that fits for every TRUE combination and combine them into an OR-sentence. I learned that trick some time ago, but I forgot
This signature is ruining eSports.
imDerek
Profile Blog Joined August 2007
United States1944 Posts
March 26 2009 17:27 GMT
#9
Use a K-map
Least favorite progamers: Leta, Zero, Mind, Shine, free, really <-- newly added
Shivaz
Profile Blog Joined March 2009
Canada1783 Posts
March 26 2009 17:33 GMT
#10
On March 27 2009 02:27 imDerek wrote:
Use a K-map


Beat me to it,

[image loading]

Track
Profile Blog Joined May 2006
United States217 Posts
March 26 2009 17:42 GMT
#11
Would you guys care to explain that algorithm and k-map?
Strength does not come from physical capacity. It comes from an indomitable will.
Malongo
Profile Blog Joined November 2005
Chile3472 Posts
March 26 2009 18:07 GMT
#12
On March 27 2009 02:42 Track wrote:
Would you guys care to explain that algorithm and k-map?

I guess you N E E D the help
On March 27 2009 01:52 StRyKeR wrote:
guess if you can find the algorithm with this hint

Assuming that this is the distribution

p q r | value
F F F | F
F F T | F
F T F | T =============> T
F T T | F
T F F | F
T F T | T =============> T or
T T F | F
T T T | T =============> T
-------------------------------------
f(p,q,r)= T


f(p, q, r) = (-p and q and -r) or (p and -q and r) or (p and q and r)


Help me! im still improving my English. An eye for an eye makes the whole world blind. M. G.
Khaymus
Profile Blog Joined June 2008
United States750 Posts
March 26 2009 18:28 GMT
#13
My brain hurts
Let them say we lived in the time of Boxer, Emperor of Terran. Let them say we lived in the time of Nal_rA, Dreamer of Protoss. Let them say we lived in the time of Savior, Master of the Zerg.
Carnivorous Sheep
Profile Blog Joined November 2008
Baa?21242 Posts
Last Edited: 2009-03-26 18:55:12
March 26 2009 18:54 GMT
#14
So you guys are doing his homework for him? Didn't know TL changed its attitudes towards people asking for homework "help."

I got 2 LA papers and a physics lab that I'd be much obliged if ya'll would do for me, thanks you, come again.
TranslatorBaa!
Pawsom
Profile Blog Joined February 2009
United States928 Posts
March 26 2009 18:56 GMT
#15
This is pretty trivial stuff for anyone that's taken even an entry level course in logic/boolean algebra no?
IntoTheWow
Profile Blog Joined May 2004
is awesome32274 Posts
March 26 2009 19:04 GMT
#16
KARNAUGHT MAPS!
Moderator<:3-/-<
IntoTheWow
Profile Blog Joined May 2004
is awesome32274 Posts
March 26 2009 19:04 GMT
#17
On March 27 2009 03:56 Pawsom wrote:
This is pretty trivial stuff for anyone that's taken even an entry level course in logic/boolean algebra no?


yes
Moderator<:3-/-<
Track
Profile Blog Joined May 2006
United States217 Posts
March 26 2009 22:29 GMT
#18
They're not doing my homework for me, smartass. I asked for help on a problem; that's hardly disallowed. And yeah, it's elementary logic because I'm in an elementary logic course in university.
Strength does not come from physical capacity. It comes from an indomitable will.
Pawsom
Profile Blog Joined February 2009
United States928 Posts
March 27 2009 02:36 GMT
#19
On March 27 2009 07:29 Track wrote:
They're not doing my homework for me, smartass. I asked for help on a problem; that's hardly disallowed. And yeah, it's elementary logic because I'm in an elementary logic course in university.

I think people jumped on you because the title made it seem like it would be an interesting, challenging question that would provoke a lot of thought, and in reality, it was just a pretty basic homework problem.
JeeJee
Profile Blog Joined July 2003
Canada5652 Posts
Last Edited: 2009-03-27 03:19:02
March 27 2009 03:13 GMT
#20
On March 27 2009 04:04 IntoTheWow wrote:
KARNAUGHT MAPS!



wait, was that paragraph about "theres a simple method lulz" part of the question, or something that you are telling us? because if it's the latter, i don't see why you need help, but if it's the former, isn't it just a homework thread?

anyway k-maps rule

edit: wait nevermind i just noticed you said you copied it all verbatim.. so i guess it's just a hw thread. look up k-maps on wiki, learn how to construct them (make sure each side-by-side differ by one bit at the most.. dont do the rookie 00 01 10 11 mistake), and just group them and simplify. takes like 30 seconds
(\o/)  If you want it, you find a way. Otherwise you find excuses. No exceptions.
 /_\   aka Shinbi (requesting a name change since 27/05/09 ☺)
1 2 Next All
Please log in or register to reply.
Live Events Refresh
Replay Cast
02:00
LiuLi 40 / Enki Pro Series 5
Liquipedia
Online Event
00:00
LATAM SC2 League: Semifinals
Liquipedia
GSL
23:00
Replay Cast
Rogue vs GuMiho
Maru vs Solar
LiquipediaDiscussion
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
Nina 232
ROOTCatZ 214
RuFF_SC2 173
StarCraft: Brood War
Rain 2499
Sea 1746
PianO 280
Leta 67
Noble 41
Terrorterran 21
Icarus 8
Dota 2
monkeys_forever356
LuMiX1
League of Legends
JimRising 763
Counter-Strike
Stewie2K683
Heroes of the Storm
Khaldor142
Other Games
summit1g10798
C9.Mang01017
hungrybox569
WinterStarcraft308
ViBE223
ToD158
Maynarde126
Mew2King75
CosmosSc2 23
Organizations
Other Games
gamesdonequick1167
BasetradeTV71
StarCraft 2
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
sctven
[ Show 16 non-featured ]
StarCraft 2
• Berry_CruncH308
• Hupsaiya 73
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• Azhi_Dahaki15
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
League of Legends
• Doublelift5912
• Lourlo1006
• Stunt265
Upcoming Events
GSL Code S
5h 30m
herO vs Zoun
Classic vs Bunny
The PondCast
6h
Replay Cast
20h
WardiTV Invitational
1d 7h
OSC
1d 9h
Korean StarCraft League
1d 23h
SOOP
2 days
sOs vs Percival
CranKy Ducklings
2 days
WardiTV Invitational
2 days
Cheesadelphia
2 days
[ Show More ]
CSO Cup
2 days
GSL Code S
3 days
Sparkling Tuna Cup
3 days
Replay Cast
3 days
Wardi Open
4 days
Replay Cast
4 days
Replay Cast
5 days
RSL Revival
5 days
Cure vs Percival
ByuN vs Spirit
RSL Revival
6 days
herO vs sOs
Zoun vs Clem
Replay Cast
6 days
Liquipedia Results

Completed

CSL Season 17: Qualifier 2
BGE Stara Zagora 2025
Heroes 10 EU

Ongoing

JPL Season 2
BSL 2v2 Season 3
BSL Season 20
KCM Race Survival 2025 Season 2
NPSL S3
Rose Open S1
CSL 17: 2025 SUMMER
2025 GSL S2
BLAST.tv Austin Major 2025
ESL Impact League Season 7
IEM Dallas 2025
PGL Astana 2025
Asian Champions League '25
BLAST Rivals Spring 2025
MESA Nomadic Masters
CCT Season 2 Global Finals
IEM Melbourne 2025
YaLLa Compass Qatar 2025
PGL Bucharest 2025
BLAST Open Spring 2025

Upcoming

Copa Latinoamericana 4
CSLPRO Last Chance 2025
CSLPRO Chat StarLAN 3
K-Championship
SEL Season 2 Championship
Esports World Cup 2025
HSC XXVII
Championship of Russia 2025
Murky Cup #2
Esports World Cup 2025
BLAST Bounty Fall 2025
BLAST Bounty Fall Qual
IEM Cologne 2025
FISSURE Playground #1
TLPD

1. ByuN
2. TY
3. Dark
4. Solar
5. Stats
6. Nerchio
7. sOs
8. soO
9. INnoVation
10. Elazer
1. Rain
2. Flash
3. EffOrt
4. Last
5. Bisu
6. Soulkey
7. Mini
8. Sharp
Sidebar Settings...

Advertising | Privacy Policy | Terms Of Use | Contact Us

Original banner artwork: Jim Warren
The contents of this webpage are copyright © 2025 TLnet. All Rights Reserved.