In a family, there are six members A, B, C, D, E and F. A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How is F related to A?

Introduction / Context:

This question mixes information about marriage, siblings, and in-law relations. You must identify the role of F with respect to A by carefully tracking who is married to whom and how B becomes the daughter-in-law of F. Problems like this train you to recognize relationships like mother, mother-in-law and grandmother in a multi-person family tree.

Given Data / Assumptions:

• There are six members: A, B, C, D, E and F.
• A and B are a married couple, with A as the male member (A is the husband, B the wife).
• C is the brother of A.
• D is the only son of C (so C is male and D is male).
• E is the sister of D (so E is female and also a child of C).
• B is the daughter-in-law of F.
• F's husband has died, so F is a widow and thus female.
• We must find how F is related to A.

Concept / Approach:

The crucial relationship is that B is F's daughter-in-law. A daughter-in-law is the wife of one's son. Since B is married to A, B is the wife of A. Therefore, F's son must be A. If B is F's daughter-in-law by virtue of being married to A, then F must be A's mother. This is the standard pattern in such problems: "X is the daughter-in-law of Y" usually implies "Y is the parent of X's husband."

Step-by-Step Solution:

Step 1: From "A and B are a married couple, A being the male member", identify A as the husband and B as the wife. Step 2: From "B is the daughter-in-law of F", we know that B is married to F's son. A daughter-in-law is always the wife of someone's son. Step 3: Since B is married to A, B can only be the daughter-in-law of F if A is F's son. Step 4: From "whose husband has died", we know F is a widow, so F is female. That confirms F is in the parent generation above A. Step 5: Therefore, F is the mother of A. Step 6: The question asks: "How is F related to A?" The clear answer is that F is A's mother.

Verification / Alternative check:

We can place everyone in a family diagram. Put F and her late husband in the top generation. They have at least one son, A, and possibly another son C (brother of A). A marries B, making B the daughter-in-law of F. C, A's brother, has two children D (son) and E (daughter). All these relationships fit the given statements perfectly:

• A and B are a married couple.
• C is the brother of A.
• D is C's son, and E is D's sister.
• B is F's daughter-in-law, and F is a widow.

In this structure, F is clearly the mother of A.

Why Other Options Are Wrong:

F cannot be A's sister, because F is in an older generation and is the one whose son is married to B.

F is not A's mother-in-law; that role would belong to B's mother, but here it is B who is the daughter-in-law of F, not A.

"None of these" is incorrect because "mother" fits exactly and is available as an option.

Common Pitfalls:

Students sometimes mistake "daughter-in-law of F" as indicating that F is the mother of B, but daughter-in-law means the woman has married F's son, not that she is F's biological daughter. Always remember: daughter-in-law is on the child's spouse side, and to identify F's exact role, you must go through the son whose wife B is. Once you recognize that A is that son, the relationship F → A as mother is straightforward.

Final Answer:

F is A's mother.