In the question some symbols -:, #, /, ¥, $\beta$ and * are used with the following meaning as illustrated below: '$P:Q$' means '$Q$ is father of $P$' '$P\#Q$' means '$P$ is mother of $Q$' '$P/Q$' means '$P$ is sister of $Q$' '$P¥Q$' means '$Q$ is brother of $P$' '$P\beta Q$' means '$P$ is wife of $Q$' '$P*Q$' means '$Q$ is wife of $P$' Which of the following expressions mean $L$ is sister-in-law of $X$?

### Concept & Blood Relation Coding In coded blood relation problems, the most critical step is noting the "direction" of the relation (e.g., does $P¥Q$ define $P$ or $Q$?) and the gender implied by the symbol. To find where $L$ is the sister-in-law of $X$, $L$ must be a female and married to a sibling of $X$ (or be the sister of $X$'s spouse). ### Step-by-Step Solution Let's evaluate the options to find the relationship between $L$ and $X$: * **Option (a):** $X ¥ H : C ¥ L$ * $C ¥ L \rightarrow L$ is the brother of $C$. * Because $L$ is defined as a brother, $L$ is male. A male cannot be a sister-in-law. (Eliminated) * **Option (b):** $L / X \beta T ¥ E$ * $L / X \rightarrow L$ is the sister of $X$. * Being the direct sister is a blood relation, not an "in-law" relation. (Eliminated) * **Option (c):** $L / X ¥ F ¥ G$ * $L / X \rightarrow L$ is the sister of $X$. * Same as above, $L$ is a sister, not a sister-in-law. (Eliminated) * **Option (d):** $L \beta G ¥ X * C$ * $L \beta G \rightarrow L$ is the wife of $G$. (This establishes $L$ as female, and $G$ as her husband). * $G ¥ X \rightarrow X$ is the brother of $G$. (This means $G$ and $X$ are brothers). * Combining these facts: $L$ is married to $G$, and $G$ is the brother of $X$. * Therefore, $L$ is the wife of $X$'s brother. The wife of a brother is exactly a sister-in-law. ### Exam Strategy & Shortcut Use **Gender and Generation Elimination** to solve these in seconds. "Sister-in-law" means $L$ MUST be female. In option (a), $C ¥ L$ makes $L$ a male (brother). In options (b) and (c), the expression starts with $L / X$, which explicitly states $L$ is the direct sister of $X$. You can instantly eliminate (a), (b), and (c) without drawing any family tree, leaving only (d) to verify. ### Common Pitfall Failing to read the "direction" of the relation. Notice that while $P \beta Q$ means $P$ is the wife of $Q$ (Left-to-Right), the symbol $P ¥ Q$ means $Q$ is the brother of $P$ (Right-to-Left). Assuming all relations flow in the same direction is the leading cause of incorrect family trees. ### Final Answer Therefore, the correct answer is **$L \beta G ¥ X * C$**.