Question 1192134
Here's how to simplify the function F(W, X, Y, Z) = X'Y' + XYZ' + WXY + W'X'Y' + WZ using a K-map:

1. **Set up the K-map:**

```
          WZ
      00  01  11  10
WX 00  1   1   1   1  (X'Y')
   01  0   0   1   0  (XYZ')
   11  0   1   1   0  (WXY)
   10  1   1   1   1  (W'X'Y' and WZ)
```

2. **Fill in the K-map:**

* X'Y' (W=0, X=0, Y=0): This covers the first row (00) entirely, regardless of Z.
* XYZ' (X=1, Y=1, Z=0): This is the cell at WX=01, YZ=10.
* WXY (W=1, X=1, Y=1): This is the cell at WX=11, YZ=11.
* W'X'Y' (W=0, X=0, Y=0): This is already covered by X'Y'.
* WZ: This term covers all cells where W=1 *or* Z=1.  The cells where W=1 are already covered by WXY and a portion of X'Y'. The cells where Z=1 are on the 01 and 11 columns.

3. **Group the 1s:**  We want to make the largest possible groups of 1s, where the groups are powers of 2 (1, 2, 4, 8, 16).

* **Group 1:** The entire first row (X'Y') is a group of 4. This represents X'Y'.
* **Group 2:** The 1s in the bottom row (W=1) are best grouped as a group of 4 (covering WZ). This represents W.
* **Group 3:** The remaining '1' at WX=01 and YZ=10 is covered by XYZ'.

4. **Write the simplified expression:**

By combining the groups, we get the simplified Boolean expression:

F(W, X, Y, Z) = X'Y' + W + XYZ'

Therefore, the simplified function is **F(W, X, Y, Z) = X'Y' + W + XYZ'**.