Consider the circuit above. Which one of the following options correctly…

Approach: use the 2:1 multiplexer identity F = s·D1 + s'·D0 and read the connections.

• Identify the lower multiplexer select as x. So f = x·D1 + x'·D0, where D1 is the data input used when x = 1 and D0 when x = 0.

• When x = 0 the circuit output equals y'·z, so D0 = y' z.

• When x = 1 the circuit output is 1, so D1 = 1. (Equivalently the upper multiplexer implements z' + y = 1 in the context of x = 1, yielding D1 = 1.)

• Thus f = x·1 + x'·(y' z) = x + x' y' z.

• Simplify using absorption: x + x' y' z = x + y' z.

• Expand x + y' z to match the original option form: x + y' z = xz' + xy + y' z, so the function is xz' + xy + y' z.

Final answer: f(x,y,z) = xz' + xy + y'z (equivalently f = x + y' z).