Question

Directions: The symbols %, @ and \# are used with the following meanings: A % B \(\rightarrow\) A is greater than B, A @ B \(\rightarrow\) A is either greater than or equal to B, A \# B \(\rightarrow\) A is smaller than B.
Statement: X%Y, Y\#V, W%Z, X@Z
Conclusions: I) Y%W, II) X\#Z

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

Hint:

A conclusion is only true if it holds in all possible scenarios permitted by the statements. If you can find even one counterexample, the conclusion is false.

Answer 1

The Correct Option is D

Step 1: Translate the statement. X \textgreater Y, Y \textless V, W \textgreater Z, X \(\geq\) Z.
Step 2: Combine the relationships where possible.
We can form a partial chain: W \textgreater Z \(\leq\) X \textgreater Y.
We also know Y \textless V.
Step 3: Evaluate the conclusions.
- Conclusion I: Y % W \(\rightarrow\) Y \textgreater W. From our chain, there is no defined relationship between Y and W. They could be anything relative to each other. Conclusion I is false.
- Conclusion II: X \# Z \(\rightarrow\) X \textless Z. The statement explicitly gives X @ Z, which means X \(\geq\) Z. This directly contradicts the conclusion. Conclusion II is false.