Discussion
Statement:
U % B, B % T, U % W, H & C, K $ U, C @ K
Conclusion:
(a) H & T (b) K @ T (c) C * B (d) W % K
Answer: E
Correct answer: None of these
This set’s code reads \(\&\) as “not greater than”, so \(\le\); \(*\) as “not smaller than”, so \(\ge\); \(\%\) as “neither greater than nor equal”, so \(<\); \(\$\) as “neither smaller than nor equal”, so \(>\); and \(@\) as \(=\). The statements become \( U < B \), \( B < T \), \( U < W \), \( H \le C \), \( K > U \) and \( C = K \).
Every relation here has U at the bottom: B, W and K all stand above it, and T stands above B while H sits below C, which equals K. So the diagram is a fan of branches rising out of U, and elements on different branches of such a fan are never ordered.
(a) \( H \le T \): H hangs below the K branch, T stands at the top of the B branch. Not determined.
(b) \( K = T \): different branches again, and nothing forces equality. Not determined.
(c) \( C \ge B \): C equals K, which is on one branch, and B is on another. Not determined.
(d) \( W < K \): W and K are both above U on separate branches. With \( U = 1 \), \( W = 2, K = 9 \) and \( W = 9, K = 2 \) both satisfy every statement. Not determined.
None of the four follows.
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