"Whenever the ambient temperature drops below $0^\circ\text{C}$ and relative humidity exceeds $90\%$, frost forms on citrus orchards. Yesterday morning, frost formed on the citrus orchard."
Which of the following conclusions CANNOT be drawn with absolute logical certainty?
Options:
(A) The ambient temperature yesterday morning was strictly below $0^\circ\text{C}$.
(B) The relative humidity yesterday morning strictly exceeded $90\%$.
(C) If frost did not form, then either temperature was $\ge 0^\circ\text{C}$ or relative humidity was $\le 90\%$.
(D) Frost on citrus orchards can only form when relative humidity exceeds $90\%$.
Answer Key:
A, B, D
Step-by-Step Solution & Explanation
The conditional rule is $(P \land Q) \implies R$. Observing $R$ (frost formed) does not allow affirming the antecedent ($P \land Q$) because other micro-climatic mechanisms or radiative cooling conditions might also cause frost (fallacy of affirming the consequent). The contrapositive $\neg R \implies \neg(P \land Q) = (\neg P \lor \neg Q)$ is logically sound (statement C). Hence, A, B, and D cannot be drawn with certainty.