Study the following information carefully. I. ‘A $ B’ means ‘A is the mother…

Concept

In coded blood-relation puzzles of this kind, the given chain is read as a complete description of one family: no relation or person exists beyond what the chain states. Each symbol denotes one fixed relation together with the implied gender of the first letter in that pair: '$' = mother of (female), '#' = father of (male), '@' = husband of (male), and '%' = daughter of (female). Because the chain is exhaustive, if two letters are joined by '@' (a marriage) and each of those two letters is separately shown as parent of a different letter elsewhere in the same chain, that married pair together count as the joint parents of both those children, so the two children are siblings of each other.

Step-by-step decoding

1. 'P % M' fixes P as the daughter of M, so M is a parent of P and P is female.

2. 'M @ N' fixes M as the husband of N, so M is male, which is consistent with M being a parent who has a spouse, and N is M's wife.

3. 'N $ Q' fixes N as the mother of Q, so N is female, which is consistent with N being M's wife, and Q is N's child.

4. By the closed-chain convention stated above, since M and N are married ('M @ N') and M is independently shown as a parent of P ('P % M') while N is independently shown as a parent of Q ('N $ Q'), M and N together are the joint parents of both P and Q, so P and Q are siblings.

5. Since P was fixed as female in the first step, P is the sister of Q.

Cross-check

Re-scan the same chain for a gender clash: M is used only as 'husband' (male), N is used only as 'wife via the husband symbol' and then 'mother via the mother symbol' (female both times), and P is used only as 'daughter' (female) -- no letter is assigned two different genders across the chain, so the reading is internally consistent and the derived relationship 'P is the sister of Q' holds.