Statements: A > B ≥ L, R > B = H Conclusions: A < L R > L

Concept

In statement-and-conclusion reasoning with chained inequalities, a strict relation ('>' or '<') absorbs any '≥', '≤', or '=' link that follows it in the same chain: X > Y ≥ Z transitively gives X > Z. When two separate statements share a common term, that shared term can be used to link a relation from one statement with a relation from the other, producing a new chain that was not stated directly.

Application

1. Statement 1 gives A > B ≥ L. Since '>' absorbs the following '≥', this transitively fixes A > L.

2. Conclusion I claims A < L, which is the opposite of A > L just established, so Conclusion I does not follow.

3. Statement 2 gives R > B = H, so R > B. Statement 1 separately gives B ≥ L.

4. B is common to both statements, so chaining R > B with B ≥ L gives R > B ≥ L, which transitively fixes R > L.

5. Conclusion II claims R > L, exactly what was just established, so Conclusion II follows.

Cross-check

Confirm with concrete values satisfying both statements: let L = 1, B = 2, H = 2, A = 3, R = 4. Then A > B ≥ L reads 3 > 2 ≥ 1 (true) and R > B = H reads 4 > 2 = 2 (true). Checking the conclusions: A < L is 3 < 1, false; R > L is 4 > 1, true. This matches the transitive result — only Conclusion II holds.

Therefore only Conclusion II follows.