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: Rephrase the initial statements.X \textgreater Y, Y \textless V, W \textgreater Z, X \(\geq\) Z.
Step 2: Combine relationships.
A partial chain can be formed: W \textgreater Z \(\leq\) X \textgreater Y.
Also, Y \textless V.
Step 3: Assess the conclusions.
- Conclusion I: Y % W \(\rightarrow\) Y \textgreater W. The chain doesn't define the relationship between Y and W. Conclusion I is incorrect.
- Conclusion II: X \# Z \(\rightarrow\) X \textless Z. The initial statement is X @ Z, which means X \(\geq\) Z. Conclusion II is incorrect.