A smart heating system activates eco-mode if the outdoor temperature is below 10°C, providing that the house has also been unoccupied for at least 2 hours or vacation mode is switched on.
This can be represented by the inputs:
The logic rule can be written as: T and (U or V)T \text{ and } (U \text{ or } V)T and (U or V)
Complete the truth table by identifying the missing values for [A], [B], [C], [D], [E], and [F].
| TTT | UUU | VVV | U or VU \text{ or } VU or V | T and (U or V)T \text{ and } (U \text{ or } V)T and (U or V) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | [A] |
| 0 | 1 | 0 | [B] | 0 |
| 0 | 0 | 1 | 1 | [C] |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | [D] | 0 |
| 1 | 1 | 0 | 1 | [E] |
| 1 | 0 | 1 | 1 | [F] |
| 1 | 1 | 1 | 1 | 1 |