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[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 States24655 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 ☺)
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