Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married. P and Q are married. R is the daughter of X. S is the sister of P. Which one of the following MUST be true?
Options:
(A) R is the sister of Q
(B) S is the sister-in-law of Q
(C) X is the father of S
(D) W is married to Z
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2017 Q.62)**
**1. Intuitive Physical Setup & Given Parameters**:
- Married couples:
- $(X, Y)$ is a married couple.
- $(P, Q)$ is a married couple.
- Sibling / descent relations:
- $R$ is the daughter of $X$ (and therefore of $Y$).
- $S$ is female and is the sister of $P$.
**2. Step-by-Step Logical Derivation**:
1. **Relationship between $S$ and $Q$**:
- $P$ and $Q$ are married to each other.
- $S$ is the biological sister of $P$.
- By definition of kinship, the sister of one's spouse is one's **sister-in-law**.
- Therefore, $S$ is the sister-in-law of $Q$.
2. This relation is logically necessary and holds true regardless of the gender distribution between $P$ and $Q$.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** (R is sister of Q): ❌ False. R belongs to the family of X and Y, not P and Q.
- **(B)** (S is the sister-in-law of Q): ✅ **CORRECT**. Spouse's sister is by definition a sister-in-law.
- **(C)** (X is father of S): ❌ False. No connection given between X and S.
- **(D)** (W is married to Z): ❌ Indeterminate. No information given for W and Z.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer**: **B**
- **Exam Rule**: The sister of a person's spouse is always that person's sister-in-law.
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