Question

if the statement \if it is midnight, then the sun is not shining\ is assumed to be true, is its reverse, \if the sun is not shining, then it is midnight\, also always true?
a. yes
b. no

Explanation:

The original statement is "If it is midnight, then the sun is not shining" (let \( P \): it is midnight, \( Q \): the sun is not shining, so \( P \to Q \)). The reverse (converse) is "If the sun is not shining, then it is midnight" (\( Q \to P \)). The sun not shining can happen at other times (e.g., night, cloudy day at noon), so \( Q \to P \) is not always true.

Answer:

B. No