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).
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...