Final answer:
The statement includes both an analytic component (bachelorhood definition) and a synthetic component (astronomical fact), making it both synthetic and analytic.
Step-by-step explanation:
The compound statement "every bachelor is a man without a wife and the Earth revolves around the Sun" is a combination of an analytic statement and a synthetic statement. The first part of the statement, "every bachelor is a man without a wife," is analytic because the predicate is contained within the subject; this means that being unmarried is part of the definition of being a bachelor. The second part of the statement, "the Earth revolves around the Sun," is synthetic because this fact is not contained within the definition of the terms 'Earth' or 'Sun' but is known through empirical observation. Therefore, the correct answer is c) Both synthetic and analytic.