In a logic circuit, input A is connected to both inputs of a NOR gate to produce an output Y₁ . Similarly, input B is connected to both inputs of a second NOR gate to produce an output Y₂ . The outputs Y₁ and Y₂ are then fed as the two inputs to a third NOR gate, which produces the final output Y . The simplified Boolean expression for the final output Y is:

Step-by-step solution

A NOR gate with both inputs tied together acts as a NOT gate. For the first NOR gate, the inputs are A and A . Its output is Y₁ = A + A = A . For the second NOR gate, the inputs are B and B . Its output is Y₂ = B + B = B . These outputs are fed into the third NOR gate. The final output is Y = Y₁ + Y₂ = A + B . Applying De Morgan's theorem ( X + Y = X Y ), we get: Y = A B = A B . Answer: A B