If P $ Q means P is the father of Q; P # Q means P is the mother of Q; and P *…

Concept

In a coded blood-relation chain, each symbol must be decoded into a specific family relation, and a person's gender is fixed ONLY when a gender-specific term (father, mother, sister, brother, son, daughter, etc.) directly names them. If no statement in the chain fixes a particular person's gender, the exact relation involving that person cannot be determined, and 'data inadequate' becomes the correct choice.

Application

1. N # L → N is the mother of L. (N is female; N is one generation above L.)

2. L $ P → L is the father of P. (L is male; P is one generation below L.) Combining with step 1: N is the mother of L, and L is the father of P, so N is the paternal grandmother of P.

3. P * Q → P is the sister of Q. (P is female; P and Q are siblings, i.e., both children of L.) Since P is L's child, and P and Q are siblings, Q is also L's child — making Q, like P, a grandchild of N.

So N is definitely the grandmother of Q. What remains unknown is Q's own gender.

Cross-check

Statement 3 only establishes P's gender ('sister') and the sibling link — it says nothing about whether Q is male or female. Testing both possibilities: if Q is male, N is Q's grandmother and Q is a grandson; if Q is female, N is Q's grandmother and Q is a granddaughter. Both assignments are equally consistent with every given statement, so neither can be confirmed over the other.

Since the chain fixes N as Q's grandmother but never fixes Q's gender, the relation of Q to N cannot be determined as either grandson or granddaughter — the data is inadequate.