The truth table for the function Y=AB+A'C is as follows:
| A | B | C | A'C | AB | Y |
|---|---|---|-----|----|---|
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 | 1 |
The Karnaugh map for this function can be represented as follows:
```
\ AB 00 01 11 10
C\
0 | 0 1 0 0
1 | 0 0 1 1
```
The grouping for the Karnaugh map is a little tricky, but we can group the cells that have the value 1:
- Group 1: C=1, AB=00
- Group 2: C=0, B=1, A=0
These groups correspond to the terms in the function Y=AB+A'C.