Layered non-strict chain: Given A < B < C ≤ D = E, determine which conclusions definitely follow. Conclusions: I) B ≤ E; II) B < E.

Introduction / Context:This question mixes strict and non-strict relations and asks you to compare B against E. Because E equals D and C is no greater than D, the strict part of the chain from B up to C ensures a strict comparison to E as well.

Given Data / Assumptions:

• A < B
• B < C
• C ≤ D = E
• Conclusions: I) B ≤ E; II) B < E.

Concept / Approach:From B < C and C ≤ E (since D = E), we have B < E directly. Once B < E is proved, the weaker statement B ≤ E follows automatically.

Step-by-Step Solution:Since C ≤ D and D = E, we have C ≤ E.Given B < C and C ≤ E, transitivity yields B < E (II is true).Any strict inequality implies the corresponding non-strict one: from B < E we get B ≤ E (I true).

Verification / Alternative check:Example values: let A=1, B=2, C=3, D=4, E=4. Then B < E (2 < 4) and B ≤ E (2 ≤ 4) both hold.

Why Other Options Are Wrong:Options a/b assert only one of the two truths; d claims “either,” which undersells certainty; e contradicts the chain.

Common Pitfalls:Mixing up ≤ and = when D = E; or thinking C ≤ E prevents a strict B vs E. The strict link is between B and C, which is sufficient to make B < E.

Final Answer:If both conclusions I and II follow