From the circuit:
Top AND gate output: A⋅B
Bottom AND gate output: Aˉ⋅B (the A input passes through a NOT gate)
The OR gate combines these:
Y=(A⋅B)+(Aˉ⋅B)
Factoring out B:
Y=B⋅(A+Aˉ)
Using A+Aˉ=1:
Y=B⋅1=B
So Y is independent of A and follows B exactly.
Reading the input waveform of B:
From t=0 to t=1 s: B=1
From t=1 to t=2 s: B=1
From t=2 to t=3 s: B=0
Hence, Y is 1 from 0 to 2 s and 0 from 2 to 3 s.
This matches the waveform shown in option (2).
Hence, the correct option is (2).