3. To find an appropriate Boolean expression, trace through the circuit from left to right, writing down the output of each logic gate. For example, after passing through the first not gate, you have the value ~P.
To determine which combination of inputs the circuit recognizes, you need to determine which of the four possible inputs:
P=1, Q=1;
P=1, Q=0;
P=0, Q=1;
P=0, Q=0;
gives an output of 1.