**Statement:** Given the inequalities: $$B M F \leq P M H$$ **Conclusions:** I. $$B L$$ II. $$F

Question

**Statement:** Given the inequalities: $$B > M > F \leq P < Q, \quad L > M > H$$ **Conclusions:** I. $$B > L$$ II. $$F < H$$ Assuming the given statements are true, determine which conclusion(s) is/are definitely true.

Accepted Answer

**Solution:** 1. From the given inequalities, we have: - $$B > M > F \leq P < Q$$ - $$L > M > H$$ 2. To check conclusion I: $$B > L$$ - We know $$B > M$$ and $$L > M$$, but there is no direct comparison between $$B$$ and $$L$$. - Since both $$B$$ and $$L$$ are greater than $$M$$, their relative order cannot be determined from the given data. - Therefore, conclusion I is **not definitely true**. 3. To check conclusion II: $$F < H$$ - From the inequalities, $$M > H$$ and $$M > F$$. - But there is no direct comparison between $$F$$ and $$H$$. - $$F$$ could be equal to or less than $$H$$, or even greater, as the data does not specify. - Hence, conclusion II is **not definitely true**. 4. Since neither conclusion I nor conclusion II can be confirmed as definitely true, the correct choice is: **Answer:** Neither conclusion I nor II is true.

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