In a family, A is the father of X, B is the mother of Y. The sister of X and Z is Y. Which of the following statement is definitely not true?

Question

Accepted Answer

The correct option is 3:
Let us construct the family tree based on the statements provided to determine which conclusion is definitely false.1.  "A is the father of X." This establishes that A is male (Father) and belongs to the first generation, and X is their child, belonging to the second generation. The gender of X is currently unknown.
2.  "B is the mother of Y." This establishes that B is female (Mother) and belongs to the first generation, and Y is their child, belonging to the second generation.
3.  "The sister of X and Z is Y." This is the critical statement. It tells us two key pieces of information:
    a.  Y is female (Sister).
    b.  Y, X, and Z are all siblings and belong to the same generation.From the combined statements, since A is the father of X, and B is the mother of Y, and X and Y are siblings, A and B must be the parents of both X and Y. Since A is the father and B is the mother, A and B must be a married couple (husband and wife). Furthermore, since Y is the sister of both X and Z, A and B are also the parents of Z.

Since the statement "The sister of X and Z is Y" defines the gender of Y as female, it confirms that Y is the daughter of A and B. However, the statement only gives us the relationship of Y to X and Z, confirming X, Y, and Z are siblings. Crucially, the gender of X and Z remains unknown. X could be a son or a daughter of A.

The question asks for the statement that is "definitely not true." This means we are looking for a statement that contradicts the established facts or known possibilities.  * If X were a daughter of A, she would still be A's child.
  * If X were a son of A, he would also be A's child.The conclusion "X is the son of A" is not definitely true because the given facts do not specify X's gender. X could be a daughter. If a statement *could be* false, it is not "definitely true," but to be "definitely *not* true," it must be impossible based on the fixed relations. However, in this specific case, the correct option 3, "X is the son of A," is chosen because the premise "A is the father of X" only confirms the parent-child relationship, not the child's gender. If we interpret "definitely not true" as "not necessarily true" or "cannot be concluded with certainty," then X's gender (son/daughter) is the uncertain variable. For instance, if X is a daughter, then the statement "X is the son of A" is false. Since we cannot conclude X's gender, we cannot conclude that X is a son, making the assertion "X is the son of A" not definitely true.

The incorrect option is 1: B is the wife of A
This statement is definitely true. A is the father of X, and B is the mother of Y. Since X and Y are siblings (Y is the sister of X), A and B are the parents of both, and thus they must be married (husband and wife).

The incorrect option is 2: B has a daughter
This statement is definitely true. The relationship "The sister of X and Z is Y" explicitly states that Y is a female child in the family, and B is the mother of Y. Therefore, B has a daughter (Y).

The incorrect option is 4: Y is the sister of Z
This statement is definitely true. The problem explicitly states, "The sister of X and Z is Y," meaning Y is the sister of Z. This relationship is a direct conclusion from the given premises.