# DeMorgans law

#### mannik

Joined Nov 26, 2004
3
Hi

My teacher is a m*ron he won't (or can't) explain following:

I have to find the complement of AB. The B have a bar over (inverted but I dunno how to do it in the forum) Can somebody explain to me how this is going on?

Tommy

#### Perion

Joined Oct 12, 2004
43
Originally posted by mannik@Nov 26 2004, 08:25 AM
Hi

My teacher is a m*ron he won't (or can't) explain following:

I have to find the complement of AB. The B have a bar over (inverted but I dunno how to do it in the forum) Can somebody explain to me how this is going on?

Tommy
[post=3805]Quoted post[/post]​
Just use an apostrophe ' character after the term instead of the bar to show the complement - like, AB' which reads "A and not B"

So - DeMorgan says:

not (x and y) = (not x) or (not y)
not (x or y) = (not x) and (not y)

Or, using the ' symbol for NOT and the usual AND and OR symbol conventions, DeMorgan is written:
(xy)' = x' + y'
(x+y)' = x'y'

In other words just take the complement of each individual term and change the AND to an OR (or vice versa).

So, for the complement of AB':

(AB')' = A'+ B (complement each term and change the AND to an OR)

Let:
A = "I am stupid"
B = "I am tall"

Then:
AB' = "I am stupid and I am not tall"

The complement of the above statement could be read something like:
(AB')' = A' + B = "Either I am not tall or I am stupid"

BTW - for me, AB :lol:

Perion

#### mannik

Joined Nov 26, 2004
3
Thank you very much for your help, now it make sence here you can see my teacker's answer:

NOT(A and (NOT B)) = NOT A or NOT(NOT B) = NOT A or B

(AB) = a + (B) = A + B

But he was unable to explain it :angry:

Again thx.

Tommy

BTW you might be tall - but I don't believe that you are stupid !!

tommy

#### Perion

Joined Oct 12, 2004
43
You're welcome.

See logic is (easy)'

Best wishes,
Perion