Quick boolean algebra problem..help needed

techguy

HI,
I hope this is the right forum..
Well I am just doing a bit of revising for boolean algebra and de morgans rule and came across this in an equation.. I cant seem to work out how part 1 = part 2 or if it is even correct? COuld someone please shed some light on it? See attachment.

Thanks,
Hakko

Hobbes

http://www.boards.ie/vbulletin/forumdisplay.php?f=380

techguy

thanks hobbes I knew there was a maths forums but it was tos up as to which forum to post in..

Mutant_Fruit

Well, you know the rule for boolean algebra? Break the line, change the sign.

Also, you can add two "not's" on top of a problem without changing it. i.e. stick two more lines on top of the left hand problem so that it's
not(not(not(NOT(A) + NOT(B) + C))) (works best if you write it down )

Then just break one of the lines, change the signs of everything beneath the line that you broke. You can then remove any excess double-nots over individual letters (not(not(A))) = A, then solve the remainder using normal techniques.

Webmonkey

It isn't a valid logic statement. They are not equal.

And the breaking line changing sign is DeMorgans Theorm.

Mutant_Fruit

Webmonkey wrote:

It isn't a valid logic statement. They are not equal.

I never tried actually solving it myself. I was too lazy to work it out

And the breaking line changing sign is DeMorgans Theorm.

I had forgotten the name of the rule, i just remembered the method. It's 2 years since i've solved these kind of questions

Webmonkey

Misticles

i got part 1 to equal part 2

Mutant_Fruit

Try putting in
A = 1
B = 1
C = 0

The left side evaluates to true, the right side evaluates to false (if i'm doing this right).

Webmonkey

Yep exact same for me

techguy

Thanks guys, the notes I got 1st time round were wrong..
it should be:
(' = not)
(A'+B'+AC)' = (B'+A'+C)' (not de morgans but another rule..)

Mutant_Fruit

(A'+B'+AC)' = (B'+A'+C)'

Break it down to just this:
A' + AC = A' + C

Look at the left side, here there's both an A and A'. If A is true, the output relies solely on C being true or false. If A is false, the output is false no matter what C is.

So, you can break this down to just A' + AC = A' + C as was shown above. That make sense?

Simlarly, what would A'B + AB' break down into? *hopes he got the example right*