Analyzing Statement Sufficiency for Blood Relation Question

The question asks us to determine the relationship between Swathi and Namitha based on two given statements and decide which statement(s) are sufficient to answer the question.

Evaluating Statement I: Swathi’s husband is the only son of Namitha’s mother.

Let's break down Statement I:

• Namitha’s mother has an only son.
• This only son of Namitha’s mother is Swathi’s husband.

Consider the implications of "the only son of Namitha's mother":

• If Namitha is a male, then Namitha himself is the only son of his mother. In this case, Swathi’s husband is Namitha. This means Swathi is the wife of Namitha. The relationship is established: Swathi is Namitha's wife.
• If Namitha is a female, then the only son of Namitha’s mother must be Namitha’s brother. In this case, Swathi’s husband is Namitha’s brother. This means Swathi is the wife of Namitha’s brother. The relationship is established: Swathi is Namitha's sister-in-law.

In both likely interpretations, Statement I provides a clear and direct relationship between Swathi and Namitha (either wife or sister-in-law). Therefore, Statement I alone is sufficient to answer the question "How Swathi is related to Namitha?".

Evaluating Statement II: Swathi’s brother and Namitha’s husband are cousins.

Let's analyze Statement II:

• Swathi has a brother.
• Namitha has a husband.
• Swathi’s brother and Namitha’s husband are cousins.

For two people to be cousins, their parents must be siblings.

Let P1 be the parent of Swathi’s brother and Swathi. Let P2 be the parent of Namitha’s husband.

Statement II tells us that P1 and P2 are siblings. This means Swathi (whose parent is P1) and Namitha's husband (whose parent is P2) are related through their parents being siblings. However, this only establishes a relationship between Swathi and Namitha's husband.

We know Namitha is the wife of a person who is Swathi's brother's cousin. But how does Namitha, the wife, relate to Swathi? There are many possibilities:

• Swathi could be the cousin's sister (from parent P1).
• Namitha could be the wife of this cousin (whose parent is P2).

Knowing that Swathi's brother is cousin to Namitha's husband does not uniquely determine how Swathi is related to Namitha. For example, Swathi could be a cousin of Namitha's husband through P1, and Namitha is simply his wife. There is no direct or fixed relationship established between Swathi and Namitha. Statement II alone is not sufficient to answer the question.

Conclusion on Statement Sufficiency

• Statement I alone is sufficient because it establishes a direct relationship between Swathi and Namitha (wife or sister-in-law).
• Statement II alone is not sufficient because it only establishes a relationship between Swathi and Namitha's husband, not between Swathi and Namitha herself.

Based on the analysis, only Statement I is sufficient to answer the question.

Revision Table: Blood Relation Sufficiency

Additional Information: Understanding Blood Relations Questions

Blood relation questions in logical reasoning test your ability to decipher relationships within a family tree structure based on given clues. These questions often involve multiple statements, and you need to determine which statements are necessary or sufficient to deduce a specific relationship.

• Key Terms: Be familiar with common family terms like father, mother, son, daughter, brother, sister, uncle, aunt, nephew, niece, cousin, grandfather, grandmother, grandson, granddaughter, spouse, sibling, in-laws (sister-in-law, brother-in-law, mother-in-law, father-in-law).
• Drawing Family Trees: For complex problems, drawing a simple diagram or family tree can be very helpful. Use symbols for male ($\text{+}$), female ($\text{-}$), marriage ($\leftrightarrow$), siblings ($\longleftrightarrow$), and parent-child ($\downarrow$).
• Statement Analysis: Analyze each statement independently first to see what relationships it reveals. Then, combine statements if necessary.
• Sufficiency vs. Necessity: Sufficiency means the statement alone is enough to answer the question. Necessity means the statement is required, perhaps with others, to answer the question. In this type of question, we check for sufficiency.
• Ambiguity: Sometimes, relationships might be ambiguous (e.g., "cousin" doesn't specify if it's a maternal or paternal cousin). Pay attention to keywords like "only son" or "only daughter" which remove ambiguity.

In sufficiency questions, the goal is not necessarily to find the relationship itself, but to determine if the statement(s) provide enough information to find a *unique* or *specific* relationship.