1. The problem is to draw the logic circuit for the Boolean expression: $$ (xyz) + (x+y+z)' + (x'zy') $$ 2. Let's break down the expression into parts. - The term $xyz$ means AND of $x$, $y$, and $z$. - The term $(x+y+z)'$ means the complement (NOT) of the OR of $x$, $y$, and $z$. - The term $x'zy'$ means AND of NOT $x$, $z$, and NOT $y$. 3. Steps to build the circuit: - Create inputs $x$, $y$, $z$. - For $xyz$, use an AND gate with inputs $x$, $y$, $z$. - For $(x+y+z)'$, first use an OR gate with inputs $x$, $y$, $z$, then feed its output into a NOT gate. - For $x'zy'$, use NOT gates for $x$ and $y$ to get $x'$ and $y'$, then use an AND gate with inputs $x'$, $z$, $y'$. - Finally, use an OR gate to combine the outputs from the three terms: $xyz$, $(x+y+z)'$, and $x'zy'$. 4. The final output is from this OR gate. This logic circuit implements the given Boolean expression correctly.