M and N had four children P, Q, R, and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which of the following statements is necessarily FALSE? A. M is the grandmother of Y. B. R is the father of Y. C. W is the wife of R. D. W is the wife of P.

GATE 2019 · General Aptitude · Family Relationship · medium

Answer: W is R's wife (since Y is R's child and W's legitimate child). W cannot simultaneously be P's wife. Statement D is necessarily FALSE. Answer: D.

1. Identify Y's parents: P and R had children X and Y respectively. So R is Y's parent. Y is also a legitimate child of W, meaning W is Y's other parent. Legitimate means W is married to R.
2. Check each statement: A: M is grandmother of Y - M is R's parent, R is Y's parent, so M is Y's grandmother. TRUE. B: R is father of Y - R had child Y, so R is Y's parent (father or mother, but given context R is likely male). TRUE. C: W is wife of R - established in step 1. TRUE. D: W is wife of P - W is already wife of R (married to R). W cannot also be wife of P (each person married at most once in these problems). NECESSARILY FALSE.