Question 1191387
Here's how to simplify F(X, Y) = X' + XY' using a K-map:

1. **Set up the K-map:**  Since there are two variables (X and Y), the K-map will be a 2x2 grid:

```
      Y
   0   1
X 0  X'Y' X'Y
  1  XY'  XY
```

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

* **X'**: This term is true when X=0, regardless of the value of Y. So, we fill in both cells in the top row (X=0) with 1s.
* **XY'**: This term is true when X=1 and Y=0.  So, we fill in the cell where X=1 and Y=0 with a 1.

```
      Y
   0   1
X 0  1   1
  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).

* **Group 1:** The two 1s in the top row form a group of 2. This group represents X' (because X=0 for both cells).
* **Group 2:** The 1 at X=1 and Y=0 is already as large a group as it can be. This represents XY'.

4. **Write the simplified expression:**

The simplified expression is simply the sum of the groups:

F(X, Y) = X' + XY'

In this particular case, the function is *already simplified*. The K-map just confirms that there are no further simplifications possible.