Family Relations Analysis: Identifying the False Statement

In this logical reasoning question, we are presented with a scenario involving five individuals, P, Q, R, S, and T, who are all part of the same family. Our task is to understand their interrelationships and then identify which of the given statements is definitively false based on the established family structure.

Establishing Family Relationships

Let's systematically deduce the relationships based on the information provided:

• P is the brother of S: This tells us that P and S are siblings. We know P is male. S's gender is not yet specified; S could be male (P's brother) or female (P's sister).
• Q is the wife of P: This means P and Q are a married couple, and Q is female.
• R and T are the children of the siblings P and S respectively:
  • R is the child of P. Since P is married to Q, R is the child of both P and Q.
  • T is the child of S. This implies S is the parent of T.

Evaluating Each Statement for Falsity

Now, let's examine each statement provided in the options and determine if it is necessarily false given the family relationships we have established:

Statement 1: S is the aunt of R

• R is the child of P.
• S is the sibling of P.
• If S is a female sibling of P (i.e., P's sister), then S would be the aunt of R (P's child).
• Since S's gender is not specified as male, S can be female. Therefore, this statement can be true and is not necessarily false.

Statement 2: S is the aunt of T

• T is the child of S. This means S is the parent of T.
• An aunt is defined as the sister of one's parent.
• Since S is already T's parent, S cannot also be T's aunt. A person cannot be their own child's aunt or uncle.
• Therefore, this statement is necessarily FALSE.

Statement 3: S is the sister-in-law of Q

• Q is the wife of P.
• S is the sibling of P.
• If S is female (P's sister), then S is the sister of Q's husband (P). A husband's sister is a sister-in-law.
• Alternatively, if S is male (P's brother), then S's wife (if he were married) would be Q's sister-in-law. However, in this specific family structure, Q is directly related to S through P.
• Given that S is P's sibling and Q is P's wife, if S is female, then S is Q's sister-in-law. Since S's gender is not restricted to male, S can be female. Therefore, this statement can be true and is not necessarily false.

Statement 4: S is the brother of P

• P is the brother of S.
• This indicates that P is male and S is P's sibling.
• S could be either male (P's brother) or female (P's sister).
• If S happens to be male, then S is indeed the brother of P.
• Therefore, this statement can be true and is not necessarily false.

Conclusion on the Necessarily False Statement

Based on our detailed analysis, the statement "S is the aunt of T" is the only statement that must be false. This is because T is explicitly stated to be the child of S, meaning S is T's parent. A parent cannot concurrently be their child's aunt.