**Statement:** Given the following coded inequalities: $$6779 5862

Question

**Statement:**

Given the following coded inequalities:

$$6779 > 5862 < 8241 = 5789, \, 5789 \geq 7145 = 3914$$

**Conclusions:**

I. $$6779 < 5789$$

II. $$3914 \geq 8241$$

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

Accepted Answer

**Solution:** 1. Analyze the given coded inequalities step-by-step: - From $$6779 > 5862 < 8241 = 5789$$, the symbol '<' between 5862 and 8241 means $$5862 < 8241$$, and '=' between 8241 and 5789 means $$8241 = 5789$$. - From $$5789 \geq 7145 = 3914$$, the symbol '=' between 7145 and 3914 means $$7145 = 3914$$, and $$5789 \geq 7145$$ means $$5789 \geq 7145$$. 2. From the above, we have: - $$8241 = 5789$$ implies $$8241 = 5789$$ (both are equal). - $$7145 = 3914$$ implies $$7145 = 3914$$ (both are equal). 3. Now, check the conclusions: - Conclusion I: $$6779 < 5789$$ Given $$6779 > 5862$$ and $$5862 < 8241 = 5789$$, so $$6779 > 5862$$ and $$5862 < 5789$$, but no direct comparison between $$6779$$ and $$5789$$ is given. Since $$6779 > 5862$$ and $$5862 < 5789$$, it does not necessarily imply $$6779 < 5789$$. So, conclusion I is **not definitely true**. - Conclusion II: $$3914 \geq 8241$$ Given $$7145 = 3914$$ and $$8241 = 5789$$, but no direct comparison between $$3914$$ and $$8241$$ is provided. Since $$7145 = 3914$$ and $$8241 = 5789$$, and $$5789 \geq 7145$$, it implies $$5789 \geq 7145$$, but this does not imply $$3914 \geq 8241$$. So, conclusion II is **not definitely true**. 4. Therefore, neither conclusion I nor conclusion II is definitely true based on the given information. **Answer:** Neither conclusion I nor II is true

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