Math Is Fun Forum

NRG

Member

Registered: 2011-03-24

Posts: 3

Boolean algebra.

Hi guys,

I'm trying to show this equivalence using boolean algebra, but I'm completely stumped. (I've spent about 20 hours and have got nowhere).

Any clues on where to start? I've tried rewriting -> as a first step as well as extended de morgan(i), but I've been at this for so long now I'm beginning to wonder whether de morgan was lying.

Regards

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Boolean algebra.

Hi NRG,

Did you try:

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"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

NRG

Member

Registered: 2011-03-24

Posts: 3

Re: Boolean algebra.

Hi,

Yes, that has been the first step I have taken in most of my attempts. (It seems like this is just trial and error..)

So I have this:

Step 1: re-writing ->

(And that's more or less where I come undone.)

Step 2: Extended De Morgan(i)

I think I'm negating wrong with that step, I don't know whether to negate the whole expression like I have, or to negate p(x) and (-qx or r(x) separately, or to negate each term separately.

I've tried all of those anyway..

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Boolean algebra.

Hi,

I don't remember the name of the rules!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

NRG

Member

Registered: 2011-03-24

Posts: 3

Re: Boolean algebra.

Hi,

-------------------------------------------------------------------------

I don't remember the name of the rules!

Thanks!

The line is where I was getting stuck every time. I was not applying De Morgan's law here because I thought that since p(x) was preceded by ¬ I was not allowed!

Using what you've written I've finally understood that the law applies to single.. as well as boolean expressions such as ¬p(x)

Thanks again.

NRG

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Boolean algebra.

Hi NRG,

You're welcome. Good to know that you understood.
Double negations simply cancel out.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."