M and N are a couple who have two children, A and B. F is the spouse of B, and D is the child of F. P is the son-in-law of N, and K is the child of P. Based on these relationships, who is the male child of M and N?

Introduction / Context:
This question is a family-relationship puzzle. You must track who is married to whom and use the phrase “son-in-law” to infer genders and relationships. The aim is to identify which child of M and N is the male child based on the given clues.

Given Data / Assumptions:

• M and N are parents of two children: A and B.

• F is the spouse of B. So B is married to F.

• D is a child of F (and hence also a child of B).

• P is the son-in-law of N, so P is male and married to one of N's children (A or B).

• K is the child of P, so K is a grandchild of M and N through P and their child.

• We assume monogamous relationships and the usual meaning of “son-in-law”.

Concept / Approach:
The word “son-in-law” indicates a male person married to someone's daughter. Therefore, the child of M and N who is married to P must be female. Since B is already married to F, P must be married to the other child, A. From this we can deduce the gender of A and then infer the gender of B.

Step-by-Step Solution:
Step 1: Because P is described as the “son-in-law” of N, P is a male married to one of N's children. Step 2: N's children are A and B. So P must be married either to A or to B. Step 3: However, F is already given as the spouse of B. That means B's spouse is F, not P. Step 4: Therefore, P cannot be married to B. The only remaining possibility is that P is married to A. Step 5: Since P is a son-in-law (male), P must be married to a daughter of M and N. Hence, A is female. Step 6: M and N have two children, A (female) and B. Thus, B is the remaining child and must be the male child.

Verification / Alternative check:
We can summarise the situation: • P is son-in-law → married to a daughter of M and N. • B is already married to F, so P must be married to A. • Therefore, A is the daughter, and B is the son. This is consistent with all given relations: D is a child of F (and B), and K is a child of P (and A), making both D and K grandchildren of M and N. No contradictions arise from this assignment.

Why Other Options Are Wrong:
Option B (“A”) is wrong because A is married to P, who is explicitly called a son-in-law, meaning A must be a daughter, not a son.
Option C (“None of their children is male”) is wrong because we have precisely one child left (B) after identifying A as female, and the family clearly includes a male child.
Option D (“Cannot be determined”) is wrong because the information about P being a son-in-law, along with B's spouse being F, is sufficient to determine the gender of both A and B.

Common Pitfalls:
A common mistake is to assume genders based purely on names instead of logical clues, or to forget that one child is already married to F. Some also overlook the fact that “son-in-law” necessarily implies a daughter on the other side of the marriage. Always prioritise the logical implications of relationship terms over any assumptions about names.

Final Answer:
Thus, the male child of M and N is B.