1. Problem i: Produce the truth table and Boolean equation for the scenario: "If the room temperature is above a certain threshold (T) and the fan is not turned on (F'), and someone is present in the room (P), then an alert (A) should be activated." 2. Define variables: - $T$: Room temperature above threshold (1 if true, 0 if false) - $F$: Fan is on (1 if on, 0 if off) - $F'$: Fan is not on (negation of $F$) - $P$: Someone is present (1 if true, 0 if false) - $A$: Alert activated (1 if true, 0 if false) 3. Boolean equation for alert activation: $$A = T \cdot F' \cdot P$$ 4. Truth table for problem i: | T | F | P | F' | A = T \cdot F' \cdot P | |---|---|---|----|-----------------------| | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | 0 | | 1 | 0 | 0 | 1 | 0 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | | 1 | 1 | 1 | 0 | 0 | 5. Problem ii: Produce the truth table and Boolean equation for the scenario: "If there is a power outage (P) and you don’t have a flashlight (F'), then you will be in the dark (D)." 6. Define variables: - $P$: Power outage (1 if true, 0 if false) - $F$: Have flashlight (1 if yes, 0 if no) - $F'$: Do not have flashlight (negation of $F$) - $D$: In the dark (1 if true, 0 if false) 7. Boolean equation for being in the dark: $$D = P \cdot F'$$ 8. Truth table for problem ii: | P | F | F' | D = P \cdot F' | |---|---|----|----------------| | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 |