Discussion

Answer: A

Correct answer: Only either I or II and III are true

Translating this set’s code: \(\$\) is “neither greater nor smaller”, so \(=\); \(\delta\) is “neither greater than nor equal”, so \(<\); \(\%\) is “neither smaller than nor equal”, so \(>\); \(*\) is “not smaller than”, so \(\ge\); and \(\#\) is “not greater than”, so \(\le\). The statements become \[ L > N \le T = D < A. \] N is a low point, so L on its left and A on its right are not connected by any chain.

III. \( A > N \): both sit on the right of the pivot, joined by \( N \le T = D < A \), which is strict at the last link. True.

Now take I and II together, since that is what the answer turns on. I claims \( L > A \) and II claims \( L \le A \). Neither can be established, because L and A stand on opposite sides of the pivot: with \( N = 1 \) we may have \( L = 9, A = 2 \) or \( L = 2, A = 9 \). But the two claims are exhaustive - L is either greater than A or it is not, and “not greater” is exactly \( \le \) - so one of them must hold. That is the “either…or” case, and it arises here from a complementary pair rather than from the statements settling anything.

So III is definitely true and either I or II is true, which is the keyed answer.