Question

Statements: A > B = C, D ≤E < B, F > A Conclusions: I. F > C II. D < A

1. F > C
2. D < A

• A. Only I is true
• B. Only II is true
• C. Both I and II are true
• D. Neither I nor II is true

Answer 1

Answer:

C. Both I and II are true

Analysis of the Statements

• Combined Inequality: The given statements are A > B = C, D ≤ E < B, and F > A. Combining these into a single chain gives: F > A > B = C and B > E ≥ D.
• Full Combined Chain: F > A > B = C and F > A > B > E ≥ D.

Evaluation of Conclusions

1. Conclusion I (F > C):
   • Looking at the chain F > A > B = C, there is a clear path from F to C.
   • The inequality signs are >, >, and =. Since > is the dominant operator throughout the path, F > C holds true.
2. Conclusion II (D < A):
   • Looking at the chain A > B > E ≥ D, we can establish a relationship between A and D.
   • Since A > B and B > E ≥ D, it follows that A > D, which is equivalent to D < A.
   • Therefore, this conclusion also holds true.

Key Concept

• In inequality problems, always establish a unified chain if possible.
• When moving through a chain, if you encounter the same directional sign (e.g., all > or all <), that relationship is definite.
• If you encounter conflicting signs (e.g., > and <) in a direct path, no definite relationship can be determined.