Logical deduction — apples, lemons, and oranges counts in a basket Statements: • The basket contains more apples than lemons. • There are more lemons than oranges. Question: If the first two statements are true, is the statement “The basket contains more apples than oranges” true, false, or uncertain?

Introduction / Context:This is a classic transitivity problem in inequality reasoning. When comparing quantities of three categories, we can sometimes chain the comparisons to reach a necessary conclusion about two of them. The challenge is to recognize that “more than” is a transitive relation for strict comparisons.

Given Data / Assumptions:

• Let A = number of apples, L = number of lemons, O = number of oranges.
• Premise 1: A > L.
• Premise 2: L > O.
• All counts are whole numbers (nonnegative integers).

Concept / Approach:For strict inequalities on real numbers (and therefore on nonnegative integers), transitivity holds: if x > y and y > z, then x > z. We simply apply this chain to A, L, and O to determine A vs. O. No additional assumptions are required.

Step-by-Step Solution:

Verification / Alternative check:Pick sample numbers consistent with the premises: let A = 10, L = 7, O = 3. Both premises hold, and indeed 10 > 3, confirming the derived statement. Any valid triple that satisfies A > L and L > O will automatically satisfy A > O.

Why Other Options Are Wrong:

• false: contradicts the guaranteed inequality chain.
• uncertain: would apply only if the relation were not transitive or if non-strict comparisons were involved; neither is the case here.
• both true and false / none of these: distractors that ignore the strict transitivity.

Common Pitfalls:Confusing strict “more than” with “at least as many as”, which is non-strict and can break simple transitivity patterns in edge cases. Here, “more than” is strict, so the chain is safe.

Final Answer:true