Given the following Karnaugh Map for a Boolean function F(w,x,y,z)

                                  

The correct options/answers are:
1. $\overline{x}\overline{z}+xz$
2. $\overline{w}\overline{x}\overline{y}\overline{z}+w\overline{x}\overline{y}\overline{z}+\overline{w}\overline{x}y\overline{z}+w\overline{x}y\overline{z}+xz$

Step-by-Step Analysis of the Karnaugh Map (K-Map):

Based on the provided K-map image, the map corresponds to a 4-variable Boolean function $F(w,x,y,z)$ where:
- The rows represent combinations of $wx$ in the standard Gray code sequence: $00$, $01$, $11$, and $10$.
- The columns represent combinations of $yz$ in the sequence: $00$, $01$, $11$, and $10$.

Looking at the values in the grid, we identify the cells containing 1s:
- Row $wx=00$: 1s are in columns $yz=00$ and $yz=10$.
- Row $wx=01$: 1s are in columns $yz=01$ and $yz=11$.
- Row $wx=11$: 1s are in columns $yz=01$ and $yz=11$.
- Row $wx=10$: 1s are in columns $yz=00$ and $yz=10$.

Grouping the 1s to simplify the Boolean expression:

1. Grouping the Center 1s (Quad group in the middle):
The four cells at the center are $(wx,yz)=\left\{\right(01,01),(01,11),(11,01),(11,11\left)\right\}$.
- Across rows $01$ and $11$, $w$ changes from 0 to 1 (eliminated), and $x$ remains constant at 1 ($x$ is kept).
- Across columns $01$ and $11$, $y$ changes from 0 to 1 (eliminated), and $z$ remains constant at 1 ($z$ is kept).
Combining these gives the term: $xz$.

2. Grouping the Corner 1s:
The four corners of the K-map contain 1s at .
If we simplify the corner group directly:
- Across the top row ($00$) and bottom row ($10$), $w$ changes from 0 to 1 (eliminated), and $x$ remains constant at 0 ($\overline{x}$ is kept).
- Across the leftmost column ($00$) and rightmost column ($10$), $y$ changes from 0 to 1 (eliminated), and $z$ remains constant at 0 ($\overline{z}$ is kept).
Thus, the corner group simplifies to: $\overline{x}\overline{z}$.

Combining the center and corner groups yields the fully minimized expression:
$F=\overline{x}\overline{z}+xz$

Alternative Expression Formulation:
If we write the four corner cells individually as sum-of-minterms instead of simplifying them together, we get:
- Cell (00, 00) = $\overline{w}\overline{x}\overline{y}\overline{z}$
- Cell (10, 00) = $w\overline{x}\overline{y}\overline{z}$
- Cell (00, 10) = $\overline{w}\overline{x}y\overline{z}$
- Cell (10, 10) = $w\overline{x}y\overline{z}$
Adding these individual corner minterms along with the simplified center term $xz$ yields the alternative representation:
$F=\overline{w}\overline{x}\overline{y}\overline{z}+w\overline{x}\overline{y}\overline{z}+\overline{w}\overline{x}y\overline{z}+w\overline{x}y\overline{z}+xz$