Ordered relations: Q = Z, C ≥ G, G ≥ Q, Q ≥ R. Which conclusions follow? I) G ≥ Z; II) C ≥ R.

Introduction / Context:
We combine equalities and inequalities to deduce new ones.

Given Data / Assumptions:

• Q = Z
• C ≥ G
• G ≥ Q
• Q ≥ R

Concept / Approach:
Use substitution and transitivity: if G ≥ Q and Q = Z, then G ≥ Z; if C ≥ G and G ≥ R (from G ≥ Q ≥ R), then C ≥ R.

Step-by-Step Solution:
G ≥ Q and Q = Z ⇒ G ≥ Z (I true). Q ≥ R and G ≥ Q ⇒ G ≥ R; C ≥ G ⇒ C ≥ R (II true).

Verification / Alternative check:
Pick numbers satisfying the premises (e.g., C=5, G=4, Q=3, Z=3, R=2). Both conclusions hold.

Why Other Options Are Wrong:
Not “only I” or “only II”; both follow.

Common Pitfalls:
Missing the intermediate step G ≥ R before concluding C ≥ R.

Final Answer:
If both conclusions I and II follow