Oracle® Certification – Reasoning Ability
Blood Relations – Advanced Study Notes
Audience: Students preparing for the Oracle “Reasoning Ability” certification (or any competitive exam that tests logical reasoning).
Goal: Master the theory of blood‑relation reasoning from first principles, learn how to build formal models, handle edge‑cases, and solve challenging problems with rigorous logic.
Structure
- Foundations – Basic definitions, graph representation, and distance metrics.
- Fundamental Principles – Symmetry, transitivity, hierarchy, and reciprocity.
- Formal Logic & Algorithms – How to encode relationships, compute degrees, and deduce new links.
- Edge‑Cases & Special Situations – Step‑relations, half‑siblings, adoptions, and multiple marriages.
- Challenging Problem – A multi‑step reasoning puzzle with full solution.
Tip: Keep a simple diagram (or mental “family graph”) whenever a problem gives a few relationships. This visual aid turns abstract logic into concrete reasoning.
1. Foundations
1.1 Core Terminology
| Term | Definition |
|---|---|
| Ancestor | A person who is a parent, grand‑parent, great‑grand‑parent, etc. |
| Descendant | A person who is a child, grand‑child, great‑grand‑child, etc. |
| Sibling | Two people sharing both parents. |
| Half‑Sibling | Two people sharing exactly one parent. |
| Cousin | Children of two siblings. |
| Avuncular | Relation to an uncle or aunt (child of a sibling of a parent). |
| In‑law | Relation through marriage (not blood). |
| Consanguineous | Same or related by blood. |
Note: In most reasoning problems we consider consanguineous links only. “In‑law” links are excluded unless explicitly stated.
1.2 Graph Representation
- Model a family as an undirected graph (G = (V, E)) where each vertex (v \in V) is a person, and an edge ((u, v) \in E) means “u is a parent of v” (direction can be ignored when only counting distance).
- The graph is a forest (collection of trees) because there is no cycle in legitimate blood relations.
- Distance (d(u, v)) = number of edges on the unique simple path between (u) and (v).
Example:
A / \ B C \ / DDistance between (B) and (C) = 2 (B–A–C).
Distance between (B) and (D) = 1 (B–D).
1.3 Measures of Relationship
| Relationship | Distance | Degree of Consanguinity | Example |
|---|---|---|---|
| Parent / Child | 1 | 1 | A → B |
| Sibling | 2 | 2 | B ↔ C |
| Grandparent / Grandchild | 2 | 2 | A → B → C |
| Aunt/Uncle / Nephew/Niece | 3 | 3 | A → B → C (A is aunt of C) |
| First Cousin | 4 | 4 | A → B → C → D |
| Second Cousin | 6 | 6 | A → B → C → D → E → F |
- Rule of Thumb: The degree equals the number of edges in the shortest path.
- Even distance → sibling‑type (parent–child → 2, grandparent → 2, etc.)
- Odd distance → avuncular or cousin type (parent–child–parent → 3).
2. Fundamental Principles
2.1 Symmetry
If X is a Y of Z, then Z is a Y of X (reciprocal).
- Example: If A is the son of B, then B is the father of A.
2.2 Transitivity
If X is a Y of Z and Z is a Y of W, then X is a Y of W (if Y is a linear relation like ancestor/descendant).
- Example: A is the father of B, B is the father of C → A is the grandfather of C.
Caution: Transitivity does not hold for all kinship types (e.g., sibling relation is not transitive: if A is sibling of B and B is sibling of C, A may not be sibling of C unless they share both parents).
2.3 Hierarchy
- Descendant chain: Parent → Child → Grandchild → …
- Sibling chain: Children of the same parents.
2.4 Reciprocity & Degree Additivity
The degree of relation between any two persons is the sum of their distances to a common ancestor.
- If (u) and (v) share ancestor (a), then
[ d(u,v) = d(u,a) + d(v,a) ] (since the path goes up from u to a and down to v).
3. Formal Logic & Algorithms
3.1 Encoding Relations
Let (P(x, y)) denote “x is a parent of y”.
Then:
- Child: (C(x, y) \equiv P(y, x)).
- Sibling: (S(x, y) \equiv \