In a family, A is the father of X and B is the mother of Y. The sister of both X and Z is Y. Based on this information, which of the following statements is definitely not true?

Introduction / Context:
This blood relation question asks you to identify which statement is definitely not true, given a set of family relationships. The twist is that some of the options may or may not be true depending on additional, unstated details, while one option clearly contradicts the information provided. You must focus particularly on gender clues embedded in words like father, mother and sister.

Given Data / Assumptions:

• A is the father of X, so A is male and a parent of X.
• B is the mother of Y, so B is female and a parent of Y.
• The sister of X and Z is Y. This means Y is female and is a sister to both X and Z.
• X and Z are siblings of Y; they share at least one common parent with Y.
• No explicit information is given about the father or mother of Z or about the gender of X and Z.

Concept / Approach:
The phrase the sister of X and Z is Y fixes Y's gender as female. Therefore, any statement that calls Y a son directly conflicts with that information. The other options involve possible parental or sibling relationships that are not contradicted by the given data and could be true in some valid family structure. Our job is to separate the absolutely impossible from the merely uncertain.

Step-by-Step Solution:
Step 1: From the sister of X and Z is Y, conclude that Y is female.Step 2: Because B is the mother of Y, B is female and a parent of Y. Y's father is not identified; he could be A or another person.Step 3: Since Y is a sister to X and Z, X and Z share at least one parent with Y, but it is not specified whether they share both parents or just one.Step 4: Examine each statement to see whether it must be false or whether it might be true under some assumptions.Step 5: The statement Y is the son of N calls Y a son, which directly contradicts the established fact that Y is a sister and therefore female.Step 6: Hence, Y is the son of N is definitely not true.

Verification / Alternative check:
Try to construct a family tree. Let A and B be married, and let them have children X, Y and Z. This setup satisfies A is the father of X, B is the mother of Y and Y is the sister of X and Z. In this tree, B is indeed the wife of A, so option B is the wife of A could be true. It is also possible that B is the mother of Z and that X is the sister of Z if X is taken to be female. Z is clearly a child of A if A and B are both parents. None of these statements contradicts the given information. However, in every such construction, Y is a daughter of her parents, never a son. Therefore, the claim that Y is the son of N fails in all valid arrangements.

Why Other Options Are Wrong as the "definitely not true" choice:
B is the mother of Z may or may not be true depending on whether Z shares both parents with Y; it is not ruled out by the data.X is the sister of Z can be true if X is female; the data do not specify X's gender, so this is only uncertain, not impossible.B is the wife of A is a natural and consistent assumption in many family structures that fit the clues.Z is the child of A is also compatible with a structure where A and B are parents of all three children.

Common Pitfalls:
Many learners treat all uncertain statements as definitely false, even though the puzzle only asks which one is definitely not true. The correct approach is to look for a direct gender or role contradiction. Here, the trap is not noticing that the word sister already fixes Y as female, making it impossible for her to be a son in any valid scenario. Always pay careful attention to words like son, daughter, brother and sister, as they carry both relationship and gender information.

Final Answer:
The only statement that directly contradicts the given information is Y is the son of N, so that is definitely not true.