Question 1191165
Here's the simplification of the given functions using K-maps:

**a. F(X, Y) = m2 + m3**

```
      Y
   X  0  1
   0  0  1  (m2)
   1  0  1  (m3)
```

Grouping m2 and m3, we get:

F(X, Y) = Y

**b. F(X, Y) = X + X’Y**

```
      Y
   X  0  1
   0  1  1
   1  1  1
```

Grouping all the 1s, we get:

F(X, Y) = 1

**c. F(X, Y) = X’ + XY’**

```
      Y
   X  0  1
   0  1  1
   1  1  0
```

Grouping the top row and the single 1 at X=1, Y=0 we get:

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

**d. F(X, Y, Z) = m0 + m2 + m5 + m7**

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

Grouping m0 and m2, and m5 and m7:

F(X, Y, Z) = X’Y’ + YZ

**e. F(X, Y,Z) = X’Y’Z’ + X’YZ + XY’Z + XYZ**

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

Grouping the top row, and the bottom row, we get:

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