Ordered relations: A ≥ B = C and D > C = E. Which conclusion(s) definitely follow? I) E > A; II) A < D.

Introduction / Context:We must decide whether each conclusion is forced by the premises or merely possible. If a relation can fail under some valid assignment, it does not “follow”.

Given Data / Assumptions:

• A ≥ B = C
• D > C = E

Concept / Approach:Translate equalities, then compare ranges implied for A and D relative to C (and E).

Step-by-Step Solution: From B = C and A ≥ B ⇒ A ≥ C; from C = E and D > C ⇒ D > E = C. I) E > A? Since A ≥ E(=C), E > A need not hold; indeed A can be > E. Not forced. II) A < D? We only know A ≥ C and D > C; A could be larger than D (e.g., A=10, C=5, D=6). Not forced.

Verification / Alternative check:Construct counterexamples: choose C=5, E=5, B=5. Pick A=10 (≥5), D=6 (>5). Then I false (5 > 10 is false) and II false (10 < 6 is false).

Why Other Options Are Wrong:Neither I nor II is guaranteed; so a/b/c are incorrect.

Common Pitfalls:Assuming transitivity across unrelated branches (A vs D) without a linking inequality.

Final Answer:If neither conclusion I nor II follows