Blood relations: Reasoning Ability Notes for RPF Constable

Blood Relations – Study Notes for Competitive Exams

(Reasoning Ability – Blood Relations)

1. Overview

Blood relations are the core of many reasoning puzzles in IIT‑JEE, BITSAT, UPSC, and other competitive exams.
The key is to treat each person as a node in a family graph and use the following rules to deduce unknown links.

Symbol	Meaning	Example
`ⱼ`	Person (e.g., `A`, `B`, `C`)
`ⱼ ⟶ ⱼ`	Parent → Child
`ⱼ ← ⱼ`	Child ← Parent
`ⱼ ↔ⱼ`	Sibling (both share at least one parent)
`ⱼ ↔ⱼ` (twins)	Both parents are the same and birth order is irrelevant
`ⱼ ↔ⱼ` (half‑siblings)	Share exactly one parent
`ⱼ →ⱼ`	Ancestor (any generation above)
`ⱼ ←ⱼ`	Descendant (any generation below)
`ⱼ ↔ⱼ`	Cousin (share at least one grandparent)

Rule of Inference

Transitivity: If A → B and B → C, then A → C.

Symmetry: If A ↔ B, then B ↔ A.

Parent/Child relation is directed; sibling relation is undirected.

2. Basic Relationships & Their Properties

Relationship	Directed?	Symmetry	Examples	Key Observations
Parent → Child	Yes	No	Father → Son	Child’s parent is the same for all children of that parent.
Child ← Parent	Yes	No	Son ← Father	Parent’s child is unique only if we know the child’s name.
Sibling ↔ Sibling	No	Yes	Brothers ↔ Sisters	Two persons who share at least one parent.
Cousin ↔ Cousin	No	Yes	First cousin ↔ First cousin	Two persons share at least one grandparent.
Uncle ↔ Nephew	No	No	Uncle ↔ Nephew	`Uncle = sibling of Parent` → `Uncle ← Nephew`.
Aunt ↔ Nephew	No	No	Aunt ↔ Nephew	`Aunt = sibling of Parent` → `Aunt ← Nephew`.
Grand‑Parent → Grand‑Child	Yes	No	Grandfather → Grandson	Two generations apart.
Great‑Grand‑Parent → Great‑Grand‑Child	Yes	No	Great‑Grandpa → Great‑Grandson	Three generations apart.

Tricky Point
Two people may be called “uncle” (or “aunt”) even if the person giving the title is a great‑uncle/great‑aunt; the term is often used loosely. In puzzles you must stick to the exact genealogical definition.

3. Building a Family Graph

List all given persons.
Draw directed edges for every parent‑child pair.
Add undirected edges for siblings.
Deduce indirect edges by transitivity.
Check for contradictions (e.g., a person cannot be both parent and child of the same person unless a time paradox is involved).

Example

Statement	Graph Edge
`A` is the father of `B`.	`A → B`
`B` and `C` are siblings.	`B ↔ C`
`C` is the mother of `D`.	`C → D`

From transitivity: A → B & B ↔ C → A → C. Thus A is also the father of C. Consequently, A → D (grand‑father).

4. Common Puzzle Types

Puzzle Type	Typical Question	Key Insight
Chain of relations	“If `A` is the son of `B`, and `B` is the daughter of `C`, who is `A`?`	Back‑track through parents.
Sibling‑parent mix	“`X` is the brother of `Y`, who is the daughter of `Z`. Who is the father of `X`?”	Recognize that `Y` and `X` share parents.
Cousin puzzles	“`S` is the cousin of `T`. If `S` is the son of `U`, who is `T`’s father?”	Cousins share at least one grandparent.
Great‑relation puzzles	“`P` is the great‑grand‑father of `Q`. `Q` is the aunt of `R`. Who is `P`’s relation to `R`?”	Combine great‑grand‑father and aunt/uncle relations.
Multiple family trees	“Two families are inter‑married. Find the relation between two people in different families.”	Merge trees at marriage nodes.

5. Tricky Points & Common Mistakes

Mistake	Why it Happens	How to Fix
Assuming uncles are always brothers of parents.	People use the term loosely.	Use the definition: Uncle = sibling of a parent or parent’s spouse.
Ignoring half‑siblings.	Puzzle may include “half‑brother” or “half‑sister”.	Explicitly note which parent is shared.
Mixing grand‑parent and great‑grand‑parent.	Same idea but different generations.	Count generations carefully.
Overlooking in‑law relations.	“Father‑in‑law” appears often.	Remember: Father‑in‑law = father of spouse.
Treating siblings as parents.	Two people may be siblings but one is also the child of the other’s spouse.	Keep parent/child edges separate from sibling edges.