Understanding Logic Symbols and Inequalities

This question involves decoding special symbols that represent relationships between elements, similar to mathematical inequalities. We need to translate the given statements into a usable form and then check if the provided conclusions logically follow from these statements.

Decoding the Symbols

Let's first understand what each symbol means:

• ‘P$Q’ means ‘P is smaller than Q’: P < Q
• ‘P©Q’ means ‘P is greater than Q’: P > Q
• ‘P#Q’ means ‘P is equal to Q’: P = Q
• ‘P@Q’ means ‘P is either equal to or greater than Q’: P ≥ Q
• ‘P*Q’ means ‘P is either equal to or less than Q’: P ≤ Q

Converting Statements into Inequalities

Now, let's convert the given statements using the decoded meanings:

1. Statements: R @ S @ T © U © X
2. Translation: R ≥ S ≥ T > U > X

1. Statements: T $ V $ W
2. Translation: T < V < W

Combining the Statements

We have two main inequality chains. Both chains involve the element T. We can combine them to get a clearer picture of the relationships:

• From Statement 1: R ≥ S ≥ T
• From Statement 1: T > U > X
• From Statement 2: T < V < W

Combining these gives us:

\( R \ge S \ge T < V < W \)

\( T > U > X \)

Or, we can see that T is linked to both R, S, U, X, V, and W.

Analyzing the Conclusions

We need to check if each conclusion is definitely true based on our combined statements.

Conclusion I: R © X

This translates to R > X.

From the first part of the combined statements, we have R ≥ S ≥ T, which means R ≥ T. From the second part, we have T > U > X, which means T > X.

If R is greater than or equal to T (R ≥ T) and T is strictly greater than X (T > X), then it logically follows that R must be strictly greater than X (R > X).

Therefore, Conclusion I (R > X) is definitely true.

Conclusion II: X $ W

This translates to X < W.

From the second part of the combined statements, we have T > U > X, which means X < U < T. So, X < T. From the first part of the second statement chain, we have T < V < W, which means T < W.

If X is strictly less than T (X < T) and T is strictly less than W (T < W), then it logically follows that X must be strictly less than W (X < W).

Therefore, Conclusion II (X < W) is definitely true.

Final Result

Since both Conclusion I and Conclusion II are definitely true based on the given statements, the correct option is the one stating that both conclusions are true.