Given this circuit:

http://img9.imageshack.us/img9/7859/circa.jpg

I need to find a logical formula.

I came up with this:

Is this correct? Can you simplify it to this?

Printable View

- Mar 28th 2009, 10:05 PMrelytlogic circuit formula
Given this circuit:

http://img9.imageshack.us/img9/7859/circa.jpg

I need to find a logical formula.

I came up with this:

Is this correct? Can you simplify it to this?

- Mar 28th 2009, 11:30 PMEmpSci
We have the following:

A1 = p' /\ q

A2 = p' /\ r

N3 = A1' = p v q'

N2 = A2' = p v r'

O1 = N2 v s = p v r' v s

A3 = N3 /\ O1 = (p v q') /\ (p v r' v s). - Mar 29th 2009, 09:16 AMrelyt
Ok, so coming out of N3....if ~(~p q) = p ~q ??

A1 = ~p q

A2 = ~p r

N3 = ~(~p q) = p ~q

N2 = ~(~p r) = p ~r

O1 = p ~r s

A3 = p ~q p ~r s

(p ~q) (p ~r s) - Mar 29th 2009, 06:54 PMEmpSci
Yes, you negate each proposition and reverse the junction - if it is AND it becomes OR and vice-versa.

For instance, let p = "Today is sunny" and q = "Today is raining".

Then, ~p/\q implies: "Today is NOT sunny AND Today is raining".

So, ~(~p/\q) means: NOT (Today is not sunny and today is raining), or, equivalently "Today is NOT-NOT sunny OR Today is NOT raining). That is, "Today is sunny OR NOT raining". It might be a cloudy weather...