Given the following premises:
1. All combine harvesters are diesel-powered machines.
2. Some diesel-powered machines emit particulates.
3. No particulate-emitting machine is zero-emission.
Which of the following statements MUST logically be true?
Options:
(A) No combine harvester is zero-emission.
(B) Some diesel-powered machines are not zero-emission.
(C) At least some diesel-powered machines are combine harvesters.
(D) All zero-emission machines are non-particulate-emitting.
Answer Key:
B, C, D
Step-by-Step Solution & Explanation
1. From premise 1 ("All combine harvesters are diesel-powered"), conversion by limitation (subalternation) yields "Some diesel-powered machines are combine harvesters". Hence, statement C is true.
2. From premise 2 ("Some diesel machines emit particulates") and premise 3 ("No particulate-emitting machine is zero-emission"), those diesel machines that emit particulates cannot be zero-emission. Thus, "Some diesel-powered machines are not zero-emission" (statement B is true).
3. Statement 3 is "No P is Z". By contraposition/conversion, "No Z is P", meaning "All zero-emission machines are non-particulate-emitting" (statement D is true).
4. Statement A cannot be deduced because we do not know whether the subset of combine harvesters overlaps with particulate emitters.