1. **Problem Statement:** Verify if the given Karnaugh map solutions and final expressions for the functions g and F are correct. 2. **For function g:** - Given expression: $xy + xy'z' + xy'z = xyz + xy'z' + xy'z' + xyz'$ (note: the second expression seems to have a typo with repeated terms). - Karnaugh map variables: $x$ (vertical), $yz$ (horizontal) with cells 00, 01, 11, 10. - Table values: \begin{tabular}{c|cccc} & 00 & 01 & 11 & 10 \\ \hline 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 1 \end{tabular} - Groups: - Group 1: cells (1,0), (1,2), (1,3) where function is 1. - Group 2: cells (0,2), (1,2). - Final expression given: $x'z' + xy$. 3. **Verification for g:** - Group 1 covers $x=1$ and $yz=00,11,10$ which simplifies to $xy$ (since $y$ and $z$ vary but $x=1$). - Group 2 covers $x=0$ and $yz=11,11$ (cells (0,2) and (1,2)) but (1,2) is in group 1, so group 2 effectively covers $x'=0$ and $yz=00$ which is $x'z'$. - The final expression $x'z' + xy$ matches the groups. 4. **For function F:** - Given minterms: $\Sigma(0, 2, 4, 5, 6, 7, 8, 10, 13, 15)$. - Variables: $AB$ (vertical), $CD$ (horizontal) with cells 00, 01, 11, 10. - Table values: \begin{tabular}{c|cccc} & 00 & 01 & 11 & 10 \\ \hline 00 & 1 & 0 & 1 & 0 \\ 01 & 1 & 1 & 1 & 1 \\ 11 & 1 & 1 & 1 & 1 \\ 10 & 1 & 1 & 0 & 1 \end{tabular} - Groups: - Group 1: cells (00,00), (00,01), (01,00), (01,01), (10,00), (10,01), (11,00), (11,01) - Group 2: cells (00,00), (01,00), (10,00), (11,00) - Group 3: cells (00,10), (01,10), (10,10), (11,10) - Group 4: cells (00,01), (00,11), (11,01), (11,11) - Final expression given: $BD + B'D' + A'D' + A'C'D'$. 5. **Verification for F:** - Group 1 covers columns 00 and 01 for rows 00, 01, 10, 11, which corresponds to $B D$. - Group 2 covers column 00 for all rows, which corresponds to $B' D'$. - Group 3 covers column 10 for all rows, which corresponds to $A' D'$. - Group 4 covers cells (00,01), (00,11), (11,01), (11,11), which corresponds to $A' C' D'$. - The final expression $BD + B'D' + A'D' + A'C'D'$ matches the groups. 6. **Conclusion:** Both solutions for g and F are correct based on the Karnaugh maps and groupings.