Let's solve the problem step by step: --- ### **Step 1: Understanding the MUX** The circuit uses an **8-to-1 Multiplexer**. - The inputs are labeled from \(I_0\) to \(I_7\). - The select lines are \(x\), \(y\), and \(z\) (which correspond to \(S_2, S_1, S_0\) respectively). ### **Step 2: Mapping Inputs** From the diagram, the MUX inputs are connected as follows: - \(I_0 = 1\) - \(I_1 = 1\) - \(I_2 = 0\) - \(I_3 = 1\) - \(I_4 = 0\) - \(I_5 = 0\) - \(I_6 = 1\) - \(I_7 = 1\) ### **Step 3: MAXTERMS (Canonical POS) Form** To write the function in **maxterms** (standard canonical form), we need to find the minterms where the output is **0** (i.e., where the MUX input is 0). Looking at the input assignments: - Output is 0 at \(I_2\), \(I_4\), and \(I_5\). So, the corresponding select inputs are: - \(I_2\): 010 (\(x=0, y=1, z=0\)) - \(I_4\): 100 (\(x=1, y=0, z=0\)) - \(I_5\): 101 (\(x=1, y=0, z=1\)) ### **Step 4: MAXTERM Indices** The maxterm indices are the indices where the output is 0: - \(I_2\): 2 - \(I_4\): 4 - \(I_5\): 5 ### **Step 5: Final Answer in Sigma/Pi Notation** Since the question asks for the MAXTERMS in shorthand standard (canonical) form, use the \(\Pi\) (product) notation: \[ F(x, y, z) = \Pi(2, 4, 5) \] --- ## **Final Answer** \[ \boxed{\Pi(2,4,5)} \] Or, in plain text: > **Π(2,4,5)** --- **Explanation:** - We wrote the output as 0 at \(I_2\), \(I_4\), and \(I_5\) (the positions where MUX input = 0). - The canonical maxterms form is the product of maxterms at these indices.