Given the relationships:

- S = H ≥ A ≥ P = E
- P

Question

Given the relationships:

- S = H ≥ A ≥ P = E
- P < L ≤ R ≤ E

Based on these, determine which conclusion(s) logically follow:

I. S < P
II. P < A

Accepted Answer

**Solution:**

1. Analyze the given relationships:
   - S = H ≥ A ≥ P = E
   - P < L ≤ R ≤ E

2. From the first chain, we see that *S* is equal to *H* and greater than or equal to *A*, which in turn is greater than or equal to *P*.
   - So, *S ≥ A ≥ P*.

3. From the second chain, *P* is less than *L*, which is less than or equal to *R*, which is less than or equal to *E*.

4. Since *P = E* from the first chain, and *R ≤ E*, it implies *R ≥ P*.

5. Now, evaluate the conclusions:
   - Conclusion I: *S < P*?
     - Since *S ≥ A ≥ P*, *S* cannot be less than *P*. So, Conclusion I is false.

- Conclusion II: *P < A*?
     - From the chain, *A ≥ P*, but since *A* can be equal to or greater than *P*, the statement *P < A* is true if *A* is strictly greater than *P*.
     - Given the inequality, it is acceptable to conclude *P < A*.

**Answer:** Only conclusion II is true.

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