The output $$Y$$ for the given inputs $$A$$ and $$B$$ to the circuit is :

Solution :

From the logic circuit :

Top AND gate receives inputs :

$$A \text{ and } B$$

Hence output of top gate :

$$AB$$

Bottom AND gate receives inputs :

$$\bar A \text{ and } B$$

Hence output of bottom gate :

$$\bar AB$$

These two outputs are connected to OR gate.

Therefore,

$$Y = AB + \bar AB$$

Taking $$B$$ common :

$$Y = B(A+\bar A)$$

Using Boolean identity :

$$A+\bar A = 1$$

Therefore,

$$Y = B$$

Hence output waveform follows input $$B$$ exactly.

From given waveform of $$B$$ :

$$B = 1 \quad \text{for } 0<t<2$$

$$B = 0 \quad \text{for } 2<t<3$$

Therefore,

$$Y = 1 \quad \text{for } 0<t<2$$

$$Y = 0 \quad \text{for } 2<t<3$$

Final Answer :

Output waveform is same as waveform of $$B$$.