A is father of X; B is mother of Y. The sister of X and Z is Y. Which of the following statement is necessarily not true ?

Question

Accepted Answer

To determine why Option 4 is necessarily not true, let's analyze the given information and each option:

### Given Information:
1. A is the father of X.
2. B is the mother of Y.
3. The sister of X and Z is Y.

### Analysis of Options:

1. **Option 1: B is the mother of Z.**
   - Since Y is the sister of X and Z, and B is the mother of Y, it is logical to conclude that B could also be the mother of Z. There is no information contradicting this, so this statement could be true.

2. **Option 2: X is the sister of Z.**
   - The statement mentions that Y is the sister of X and Z. However, it does not specify the gender of X. X could be either a brother or a sister to Z. Therefore, this statement is not necessarily true, but it is not necessarily false either.

3. **Option 3: B is the wife of A.**
   - A is the father of X, and B is the mother of Y. Since Y is the sister of X and Z, it is reasonable to infer that A and B are the parents of Y, X, and Z, making B the wife of A. There is no information to contradict this, so this statement could be true.

4. **Option 4: Y is the son of A.**
   - The statement specifies that Y is the sister of X and Z, indicating that Y is female. Therefore, Y cannot be the son of A. This statement is necessarily not true because it contradicts the given information about Y's gender.

### Conclusion:
Option 4 is necessarily not true because it directly contradicts the given information that Y is the sister of X and Z, indicating that Y is female. The other options do not have such contradictions and could be true based on the information provided.