Blood Relations

Blood-relation problems ask: given a chain like "A is the brother of B, B's daughter is C, C is married to D", determine the relationship between two people.

Standard relations:

• Father, mother, parents: previous generation.
• Son, daughter, children: next generation.
• Brother, sister, siblings: same generation, same parents.
• Grandfather/mother: 2 generations up. Grandson/daughter: 2 generations down.
• Uncle, aunt: parent's sibling.
• Cousin: child of uncle/aunt.
• Nephew, niece: sibling's child.
• Father-in-law, mother-in-law: spouse's parents.
• Brother-in-law, sister-in-law: spouse's sibling, or sibling's spouse.
• Son-in-law, daughter-in-law: child's spouse.

Diagram conventions (essential for accuracy):

• Draw a vertical line for parent → child.
• Horizontal line for spouses (often with a + or =).
• Use circles for females, triangles or boxes for males.
• Always label with letters as you go.

Pronoun rule — pay close attention. "His mother's brother's son" requires careful chaining:

1. His mother (woman, parent).
2. Her brother (man, same generation as mother → uncle to him).
3. His son → cousin.

So "his mother's brother's son" = his cousin.

Self-referential: "Pointing to a man, A says, 'He is the son of my grandfather's only son.'" Grandfather's only son = A's father. Son of A's father = A himself (or A's brother). If A is male, it's either A or his brother; if explicitly A's reflection in mirror, then A.

Mixed-gender trick: if the problem says "the son of B's father is C and C is married to D", then C is B's brother and D is B's sister-in-law.

Example 1:
Pointing to a photograph, Rani said, "She is the daughter of my grandfather's only son." How is the girl related to Rani?
Method: Grandfather's only son = Rani's father. His daughter = Rani's sister. Answer: sister (or Rani herself if Rani has no sister).

Example 2:
A's father is B's son. C is the paternal uncle of A and the brother of D. How is D related to B?
Method: A's father is B's son → B is A's grandfather. A's father has a brother C (since C is paternal uncle = father's brother). C is also brother of D, so D is B's child too. D's gender unstated → D is B's son or daughter.

Example 3:
P is the brother of Q. R is the sister of P. S is the mother of P. How is S related to R?
Method: P and Q are brothers (P male, Q gender unstated but treat as sibling). R is sister of P. S is mother of P, hence mother of R too. Answer: mother.

Example 4 (single-male family):
"Showing a man, Rakesh said, 'His brother's father is the only son of my grandfather.'" How is the man related to Rakesh?
Method:

• The only son of Rakesh's grandfather = Rakesh's father.
• "His brother's father" = his own father (since brothers share a father).
• So his father = Rakesh's father → he is Rakesh's brother. (Or Rakesh himself, but typically excluded.)
  Answer: Rakesh's brother.

Example 5 (in-laws):
"M is the wife of N. P is the brother of N." Then P is M's brother-in-law (husband's brother).

Tactic: when stuck, draw the tree on rough paper. Most chains feel complex but become trivial in a diagram. Label each generation clearly.