Two chains; check conclusions: Statements: H ≥ G < I F ≤ G > Z Conclusions: I. F ≤ H II. Z < I

Introduction / Context: We must synthesize two short chains that share G, then test two conclusions that compare variables across the chains.

Given Data / Assumptions:

• H ≥ G and G < I
• F ≤ G and G > Z
• Conclusions: (I) F ≤ H, (II) Z < I

Concept / Approach: Use G as the hub: compare everything to G first, then move outward via transitivity.

Step-by-Step Solution: (I) From F ≤ G and H ≥ G, we obtain F ≤ G ≤ H ⇒ F ≤ H. (II) From Z < G and G < I, we obtain Z < G < I ⇒ Z < I.

Verification / Alternative check: Try numbers: G = 5, H = 7, F = 4, Z = 1, I = 9. Then F ≤ H (4 ≤ 7) and Z < I (1 < 9) hold. Edge case H = G is also fine because non-strict relation still yields F ≤ H.

Why Other Options Are Wrong: Each denies at least one transitive consequence directly implied by the chains.

Common Pitfalls: Misreading “G < I” as “G ≤ I” (it is strict) is harmless here but, in other problems, strict vs. non-strict may change the result.

Final Answer: Both conclusions are true.