**Statement:** & $ = %, @ # **Conclusions:** I. & # II. $ ? III. % ≤ ? Assuming the given statements are true, identify which conclusion(s) is/are definitely true.

Question

**Statement:**

& > $ = %, @ < ? ≥ #, % = ! > #

**Conclusions:**

I. & > #

II. $ > ?

III. % ≤ ?

Assuming the given statements are true, identify which conclusion(s) is/are definitely true.

Accepted Answer

**Solution:** 1. From the statement, we have the following inequalities: - & > $ - $ = % - @ < ? - ? ≥ # - % = ! - ! > # 2. Let's analyze each conclusion: - **Conclusion I: & > #** - Since & > $ and $ = %, it means & > %. - % = ! and ! > #, so % > #. - Therefore, & > % > #, which implies & > #. - Conclusion I is **true**. - **Conclusion II: $ > ?** - $ = % and @ < ?. - There is no direct relation between $ (or %) and ?. - Since ? ≥ # and % > #, but no direct comparison between % and ? is given, we cannot confirm $ > ?. - Conclusion II is **not definitely true**. - **Conclusion III: % ≤ ?** - % = ! and ! > #. - ? ≥ #. - Since ! > # and ? ≥ #, % (= !) could be greater than or equal to #, but no direct comparison between % and ? is given. - So, % ≤ ? cannot be confirmed definitely. - Conclusion III is **not definitely true**. **Answer:** Only conclusion I is true.

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