Replacing F with F + 1 gives
5/9 (F + 1 - 32) = 5/9 (F - 32) + 5/9 = C + 5/9
so a temperature increase of 1º F translates to a 5/9º increase in Celsius, so I is true.
Replacing F with F + 5/9 gives
5/9 (F + 5/9 - 32) = 5/9 (F - 32) + (5/9)² = C + 25/81
so increasing the temperature by 5/9º F amounts to a 25/81º increase in Celsius, so III is false.
Solve for F in terms of C :
F = 9/5 C + 32
Replacing C with C + 1 gives
9/5 (C + 1) + 32 = 9/5 C + 32 + 9/5 = F + 9/5
and 9/5 = 1.8, so a 1º C increase translates to a 1.8º F increase, so II is also true and the answer is D.
