Question

Which of the following expressions will definitely be true if the expression \( R > O = A > S < T \) is definitely true?

• A. \( O > T \)
• B. \( S < R \)
• C. \( T < A \)
• D. \( S = O \)

Hint:

Split the chain into pairwise relations and use transitivity through the term that is common to two of them.

Answer 1

The Correct Option is B

Step 1: Break the combined statement into simple relations.
The given statement \( R > O = A > S < T \) can be split into four simple facts read left to right: \( R > O \), \( O = A \), \( A > S \), and \( S < T \).

Step 2: Combine the relations that share a common term.
Since \( O = A \), we can replace \( O \) by \( A \) in the first relation, which gives \( R > A \). We already know \( A > S \). Chaining \( R > A \) and \( A > S \) through the common term \( A \) gives \( R > S \), which is the same as saying \( S < R \). This relation comes purely from transitivity, so it holds no matter what actual numbers are picked, as long as they satisfy the original statement.

Step 3: Check why the remaining options are not guaranteed.
Option \( O > T \): we only know \( O = A > S \) and separately \( T > S \), so \( O \) and \( T \) are both greater than \( S \) but nothing links \( O \) and \( T \) directly, so this need not be true.
Option \( T < A \): in the same way, \( A \) and \( T \) are only related through \( S \), both being greater than \( S \), so no fixed relation between \( T \) and \( A \) can be pinned down.
Option \( S = O \): we already showed \( O = A > S \), which means \( O \) is strictly greater than \( S \), so \( S \) can never equal \( O \); this option is actually false, not just uncertain.

Final Answer:
Only \( S < R \) is forced to be true by this chain of relations. \[ \boxed{S < R} \]