Logical deduction – comparing battery life across three products Given: Battery X lasts longer than Battery Y. Battery Y lasts less than Battery Z. Question: If those two facts are true, is the statement “Battery Z lasts longer than Battery X” true, false, or uncertain?

Introduction / Context:
This is a classic inequality-chain problem. We know X > Y and Z > Y. That alone does not establish a direct order between X and Z. You must check if the third claim is logically forced by the premises or not.

Given Data / Assumptions:

• X > Y.
• Z > Y.
• Claim to evaluate: “Z > X.”

Concept / Approach:
From X > Y and Z > Y, X and Z are both above Y. But their relative order remains unknown; Z could be greater than, less than, or equal to X, while still keeping both greater than Y.

Step-by-Step Solution:
1) Example A: Let Y = 5, X = 8, Z = 9 ⇒ Z > X (claim True).2) Example B: Let Y = 5, X = 9, Z = 8 ⇒ Z < X (claim False).3) Since both assignments satisfy the premises, the truth of the claim cannot be determined.

Verification / Alternative check:
The uncertainty is structural: the premises do not compare X and Z directly, so the conclusion is not compelled.

Why Other Options Are Wrong:

• True / False: Each can be made true by a different consistent assignment.
• Both true and false: A single conclusion cannot have both values; instead we classify the outcome as “Uncertain.”

Common Pitfalls:
Assuming transitivity from two separate comparisons with a common middle (Y) when the necessary link between X and Z is missing.

Final Answer:
Uncertain