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: T\#B, Q%S, T%M, Q@R, U\#S, S@T
Conclusions: I) Q%T,
II) U\#T

• 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:

For coded inequalities, first translate all symbols into standard mathematical notation (\textgreater, \textless, \(\geq\), \(\leq\), =). Then, try to combine the individual statements into a single chain to easily compare the variables mentioned in the conclusions.

Answer 1

The Correct Option is A

Step 1: Translate the statement into standard inequality symbols. T \textless B, Q \textgreater S, T \textgreater M, Q \(\geq\) R, U \textless S, S \(\geq\) T.
Step 2: Combine the relationships to find connections between variables. From Q \textgreater S and S \(\geq\) T, we can create a chain: Q \textgreater S \(\geq\) T. From U \textless S and the chain above, we have U \textless S \(\geq\) T.
Step 3: Evaluate the conclusions. - Conclusion I: Q % T \(\rightarrow\) Q \textgreater T. Our chain Q \textgreater S \(\geq\) T confirms that Q must be greater than T. Conclusion I is true. - Conclusion II: U \# T \(\rightarrow\) U \textless T. Our chain U \textless S \(\geq\) T does not give a definite relation between U and T. For example, if S=10, T=8, U could be 9 (U\textgreater) or 7 (U \textless T). Conclusion II is false.