Thread: logic circuit formula

Given this circuit:



I need to find a logical formula.

I came up with this:




Is this correct? Can you simplify it to this?

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).

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)

Originally Posted by relyt

Ok, so coming out of N3....if ~(~p q) = p ~q

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...