Question 1191388
Here's how to simplify F(X, Y, Z) = m0 + m2 + m5 + m7 using a K-map:

1. **Set up the K-map:**  Since there are three variables (X, Y, and Z), the K-map will be a 2x4 grid:

```
      YZ
   00  01  11  10
X 0  m0  m1  m3  m2
  1  m4  m5  m7  m6
```

2. **Fill in the K-map based on the minterms:**

* m0: X=0, Y=0, Z=0  (top left cell)
* m2: X=0, Y=1, Z=0  (top right cell)
* m5: X=1, Y=0, Z=1  (bottom middle cell)
* m7: X=1, Y=1, Z=1  (bottom right cell)

```
      YZ
   00  01  11  10
X 0  1   0   0   1
  1  0   1   1   0
```

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).

* **Group 1:** The two 1s in the top row can be grouped together. This represents X'Z' (X=0 and Z=0 for both cells).
* **Group 2:** The two 1s in the bottom right corner can be grouped together. This represents XZ (X=1 and Z=1 for both cells).

4. **Write the simplified expression:**

F(X, Y, Z) = X'Z' + XZ

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