Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

These 3 expressions should be equivalent.

The variables a, b, c, and d can be 1 or 0, meaning true or false.

Randomly assign 1's and 0's to a, b, c, and d, and

evaluate any expression, and they should come

out to the same value of either 1 or 0 each time

you pick your random a, b, c, and d values.

The expressions will evaluate to 0 when

(a,b,c,d) = (0,0,0,0), (1,0,1,0), (1,1,1,1), or (0,1,0,1).

The other 12 assignments for (a,b,c,d) all evaluate to 1.

Expression #1

Expression #2

Expression #3

is defined as:

is defined as:

is defined as:

is defined as:

*Last edited by John E. Franklin (2008-05-10 16:02:51)*

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Here are 4 more boolean expressions that should be equivalent to each other, but different from the ones listed above.

These expressions evaluate to 1 or true when

(a,b,c,d) = (0,0,0,0), (1,0,1,0), (1,0,1,1),

(1,0,0,1), (1,1,0,1), (0,1,0,1), or (0,1,1,1).

These expressions evaluate to 0 for any other

assignments of (a,b,c,d).

Expression #1

Expression #2

Expression #3

Expression #4

*Last edited by John E. Franklin (2008-05-10 17:51:12)*

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I got poison ivy and am almost over it, and I fell down roller blading due to a crack in the road on a hill, and I wasn't wearing knee pads. That's all healed now too. I can also use <F1> or <Insert> keys to trigger my left-mouse-click button.

And <F2> and <F3> page up and down, and <tilde> button goes back in history button, so when I fold my laptop flat and hold it all vertical on the couch, I can read random Wiki articles with just using my thumb. 2 cats are sleeping on couches right now. I hear frogs making noises and it's 11PM. Maybe they want me to shut off the lights so the wetland is darker. I'm applied at a sawmill, but no luck yet. It's gonna be hard to find a job now that my job history is laiden with nothing for a year. Sure has been quite a vacation, and now I'm almost off all my meds, should be about a year if tapering goes slowly as it has been!!

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Well tapering the meds all the way last year turned out to be a bad idea since it landed me in the hospital twice in a 40 day period. The brain is a mysterious thing, and I have come down with an illness closely related to the brain processing when I hit about 30 years old twelve years ago. So now I'm back on my meds again to a pretty substantial level and now I weigh 216 lbs, but most of that is muscle luckily. My face looks thin enough, and that's important. When your face gets fat, you start to get depressed for sure. That started happening to me some years ago on meds. So now I am still researching and experimenting with various Venn diagrams involving triangles, tetrahedrons, circles and cubes and hypercubes, to further my understanding of logic and boolean algebra as it relates to digital electronics. I am lifting weights and splitting a little wood for exercise. I did work for fourteen weeks from May to August, but I worked so fast I had to take a break when I got some weird feeling in my shoulders, sort of like pitchers might get. Luckily the employer will let me go back should I choose to since they saw me working so hard, they surely believed the story I wrote in a leaving note. I also do handstands and try to swing on the jungle gym or monkey bars when I can, and I try to have fun playing my trombone, clarinet, electric guitar with the frets removed, flute, and whistling through my fingers various ways along with recorded music or the radio.

Also my only son is getting older now, and he's turning out to be quite a person, smarter than me too, without a doubt!

That's all for this post. Talk again here in a year...

*Last edited by John E. Franklin (2009-09-25 04:13:11)*

**igloo** **myrtilles** **fourmis**

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

You seem to be doing very well, despite your illness. Glad to hear from you again.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,945

Hi John E. Franklin;

Thats an amazing regimen for two people. More power to you!

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**ahmad01****Member**- Registered: 2009-09-29
- Posts: 4

I love Autumn ^_^

So Romantic...

Offline

**ahmad01****Member**- Registered: 2009-09-29
- Posts: 4

John Franklin.. ^_^

What is you Answer of your Exercise?

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Hi ahmad01,

The answer of my exercise is to stay healthy and not too heavy because it is easy to eat too much food when you take anti-psychotic medications. I've been getting lazy in the past 2 weeks, and have to up the exercise again so I don't turn into a blob. Some combinations of meds can also make you a little fatigued, so that makes exercise harder. When I am doing my best physically, then eventually it turns out I'm doing my worst mentially and end up in the mental ward again, so I'm going to talk to my psychiatrist about trying another medication instead, since there are alternatives, one that affects the Q-T interval of the heartbeat a little, but usually without any problems, and that one people sometimes even lose some weight! --John

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Eh bien, je crois que je voudrais ecrire quelque chose ici depuis cela a ete un longtemps.

I think I should have conjugated "ecrire" somehow above, but I don't know how.

If anyone finds a great conjugating francais livre avec plusier d'examples, please let me know its title.

My main langue est anglais, mais I attempt to speak le francais maintenant et then to prepare for a fun visit to Quebec again someday soon hopefully within the prochaine year or so.

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I'm gonna hit the sack for the night. Bon soir ou bonne soirree, cependant si vous rester awake or go to sleep.

**igloo** **myrtilles** **fourmis**

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,945

Pleasant dreams and welcome to the forum!

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Merci beaucoup bobby. It feels like deja vu!

**igloo** **myrtilles** **fourmis**

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,945

Howdy John;

Morning. Thought the welcome was long overdue.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Seven point four years here It says. Amazing how time flies. I wonder what I'll be doing this time 1017 lifetimes from now?

**igloo** **myrtilles** **fourmis**

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I am of the opinion that each critter, creature, and character that roams this world serves a purpose in the story of time. Imagine for a moment that even an earthworm may possess a love of self and a love of others. This may sound unlikely, yet its truth is not easily refutable unless you could put yourself into the place of the earthworm. Consider perhaps that everything, rocks, grass, and brainy creatures too are all priceless from this point forward and see what happens.

**igloo** **myrtilles** **fourmis**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Hi JEF

I'm more with the matrixers.I think life is just an illusion. You could call it matrixism

*Last edited by anonimnystefy (2012-02-26 12:22:51)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

That's an interesting point too, matrix illusion, like stuck in a computer program.

You know, there is also the world of dreaming when you are asleep.

Do you have an opinion on what might the implications of that world?

**igloo** **myrtilles** **fourmis**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Hi JEF

I'm using my phone for browsing and I didn't see the line that separates the signature from the rest of the post, so I thought that your signature was your main post.

Anyway, I wasn't thinking of it in that way exactly.I thought of it in the sense of the matrix like in the movie.Machines controlling our while lives and all that.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,945

Anyway, I wasn't thinking of it in that way exactly.I thought of it in the sense of the matrix like in the movie.Machines controlling our while lives and all that.

What if it isn't machines?

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Are you talking about the Creator?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,945

I wasn't thinking of him particularly.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Hi bobbym

Well even if the beginning of the universe did exist then I'm with futurama.maybe there was a Creator that created a particle but then the universe developed on its own.All that stuff seems very mysterious but is probably rather simple.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 95,945

A particle is the current view of physics. It is based on their passion to explain everything by inventing yet another particle.

Depends on what you mean by simple.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,922

Hi bobbym

I just think that they are making a big deal out of the whole universe thingy!

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline