1. **State the problem:** Construct the circuit for the Boolean expression $ (x+z)(y+z) $. 2. **Recall Boolean algebra rules:** - The plus sign $+$ represents the OR operation. - The multiplication (juxtaposition) represents the AND operation. 3. **Analyze the expression:** - The expression is a product (AND) of two sums (ORs): $ (x+z) $ AND $ (y+z) $. 4. **Construct the circuit step-by-step:** - First, create two OR gates: one for inputs $x$ and $z$, and another for inputs $y$ and $z$. - Then, feed the outputs of these two OR gates into an AND gate. 5. **Final Boolean expression for the circuit:** $$ (x+z)(y+z) $$ This circuit outputs 1 only when both $ (x+z) $ and $ (y+z) $ are true.