Reasoning Analysis: Statement and Conclusion Validity

This question requires us to analyze a given statement containing relational operators and determine which of the provided conclusions logically follow from it. We need to carefully trace the relationships.

Statement and Conclusions Overview

Given Statement: Y ≥ C < O ≥ F < R = B

This statement establishes the following relationships:

• Y is greater than or equal to C (Y ≥ C)
• C is less than O (C < O)
• O is greater than or equal to F (O ≥ F)
• F is less than R (F < R)
• R is equal to B (R = B)

Conclusions to Evaluate:

• I. B > F
• II. R > C

Detailed Evaluation of Conclusions

Evaluating Conclusion I: B > F

To determine if B > F is true, we look at the part of the statement connecting F, R, and B.

From the statement, we have F < R and R = B.

Since R is equal to B, we can substitute B for R in the inequality F < R.

This substitution yields F < B.

The conclusion B > F is equivalent to F < B. Therefore, Conclusion I is definitely true.

Evaluating Conclusion II: R > C

To check if R > C follows, we need to analyze the relationships connecting C, O, F, and R.

The relevant chain is C < O ≥ F < R.

We know:

• C < O
• O ≥ F
• F < R

The relationship between C and F is not definitively established by C < O ≥ F. For example, C could be less than F, or C could be greater than F (provided O is sufficiently large).

Let's test if we can find a scenario where R > C is false, while the main statement holds true. This would happen if R ≤ C.

Consider the following values:

With these values, the original statement Y ≥ 5 < 6 ≥ 4 < 5 = 5 holds true (assuming a valid Y, e.g., Y=5).

Now, let's check Conclusion II: R > C.

Substituting the values, we get 5 > 5.

This statement (5 > 5) is false.

Since we found a valid case where Conclusion II does not hold true, Conclusion II does not definitely follow from the given statement.

Summary of Findings

Our analysis shows:

• Conclusion I (B > F) is always true based on the statement.
• Conclusion II (R > C) is not always true.

Therefore, only Conclusion I follows.