3. To find an appropriate Boolean expression, trace through the circuit from left to right, writing down the output of each logic gate.
Hence, ~(P V Q) L ~Q is a Boolean expression for this circuit.
To determine which combination of inputs the circuit recognizes, you need to determine which of the four possible input combinations give an output of 1.
This circuit recognizes the input combination P=0, Q=0.
Note that this illustrates the fact that the Boolean expression ~(P V Q) L ~Q is equivalent to the Boolean expression ~P L ~Q.