Comparative reasoning about quantities watched: Josh saw more movies than Stephen, and Stephen saw fewer movies than Darren; decide, strictly from these two premises, whether the statement "Darren saw more movies than Josh" must be true.

Given data

• Premise 1: Josh > Stephen (Josh saw more movies than Stephen).
• Premise 2: Darren > Stephen (Stephen saw fewer than Darren).
• Claim to test: Darren > Josh.

Concept / ApproachTranslate the sentences into inequalities and then compare what is known and unknown.Knowing that both Josh and Darren exceed Stephen does not, by itself, order Josh and Darren relative to each other.

Step-by-step reasoningStep 1: From Premise 1, J > S.Step 2: From Premise 2, D > S.Step 3: There is no premise comparing J and D directly. Both could be greater than S, but either one could be larger.Step 4: Construct models: (a) J=12, S=10, D=15 ⇒ D > J (claim true). (b) J=16, S=10, D=15 ⇒ J > D (claim false). Since both are compatible with the premises, the claim is not entailed.

Verification / Alternative viewBecause two different consistent assignments yield opposite truth values for the claim, the truth of the claim is undetermined from the premises.

Common pitfalls

• Assuming transitivity via Stephen (e.g., "greater than Stephen" implies a chain between Josh and Darren). It does not.
• Confusing "possible" with "necessary."

Final AnswerCannot be determined from the given premises.