1. **Stating the problem:** We are given the temperature conversion formula between Fahrenheit ($F$) and Celsius ($C$): $$C = \frac{5}{9} (F - 32)$$ We need to determine which statements about temperature increases are true based on this formula. 2. **Understanding temperature increases:** The formula relates absolute temperatures, but temperature increases correspond to changes in $F$ and $C$ without the constant offset 32. 3. **Formula for temperature increase:** If $\Delta F$ is an increase in Fahrenheit, then the corresponding increase in Celsius $\Delta C$ is: $$\Delta C = \frac{5}{9} \Delta F$$ This is because the constant 32 cancels out when considering differences. 4. **Check statement I:** "A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius." Using the formula: $$\Delta C = \frac{5}{9} \times 1 = \frac{5}{9}$$ This is true. 5. **Check statement II:** "A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit." From the formula: $$\Delta C = \frac{5}{9} \Delta F \implies \Delta F = \frac{9}{5} \Delta C$$ For $\Delta C = 1$: $$\Delta F = \frac{9}{5} \times 1 = 1.8$$ This is true. 6. **Check statement III:** "A temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius." Using the formula: $$\Delta C = \frac{5}{9} \Delta F$$ If $\Delta F = \frac{5}{9}$, then: $$\Delta C = \frac{5}{9} \times \frac{5}{9} = \frac{25}{81} \approx 0.31$$ This is not equal to 1 degree Celsius, so statement III is false. **Final answer:** Statements I and II are true, so the correct choice is D) I and II only.