Given the inequality chain: $$J K \geq H = U \geq B \leq T B$$ II. $$H

Question

Given the inequality chain: $$J > K \geq H = U \geq B \leq T < F \leq R$$ Determine the truth of the following conclusions: I. $$J > B$$ II. $$H < R$$

Accepted Answer

**Solution:** 1. Given inequality chain: $$J > K \geq H = U \geq B \leq T < F \leq R$$ 2. Analyze conclusion I: $$J > B$$ - From the chain, we have $$J > K \geq H = U \geq B$$. - Since $$J > K$$ and $$K \geq H$$ and $$H = U \geq B$$, it follows that $$J > B$$. - Therefore, conclusion I is **true**. 3. Analyze conclusion II: $$H < R$$ - From the chain, $$H = U \geq B \leq T < F \leq R$$. - However, $$B \leq T$$ means $$B$$ could be equal to or less than $$T$$, so the exact relation between $$H$$ and $$R$$ is not strictly established. - Since $$H = U \geq B$$ and $$B \leq T < F \leq R$$, $$H$$ could be equal to or greater than $$B$$, but no strict inequality $$H < R$$ is guaranteed. - Therefore, conclusion II is **false**. **Answer:** (d) if only conclusion I is true.

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