👨‍👩‍👦 Blood Relations

Day 2 | ⏱️ Part of 3-Hour Reasoning Block | TCS Interview Prep

📌 Subtopics

• Family tree construction from given statements
• Identifying relationships (father, mother, uncle, cousin, etc.)
• Coded blood relations (using symbols/codes)
• Gender determination from clues

📖 Comprehensive Notes

1. Family Tree Construction

Drawing a family tree is the most structured way to solve blood relation problems.

• Standard Symbols:
  • Gender: Males $\rightarrow$ Plus ($+$) or Square ($\square$), Females $\rightarrow$ Minus ($-$) or Circle ($\bigcirc$).
  • Marriage: Double horizontal line or equal sign ($=$) connecting the spouses.
  • Siblings: Single horizontal line ($-$) connecting brothers/sisters.
  • Generations: Vertical line ($|$) connecting parent to child. The older generation is always placed higher.

  [Grandfather (+) ] = [Grandmother (-) ]
          |
     [Father (+) ] = [Mother (-) ] ---- [Uncle (+) ]
          |
     [ Self (+) ] ---- [ Sister (-) ]

2. Identifying Relationships

Be precise with English terms for relationships, which are more generic than regional names:

• Paternal: Related from father’s side (e.g., Paternal Uncle $=$ Father’s brother).
• Maternal: Related from mother’s side (e.g., Maternal Aunt $=$ Mother’s sister).
• In-Laws: Related through marriage (e.g., Sister-in-law $=$ spouse’s sister or brother’s wife).
• Nephew/Niece: Brother’s/Sister’s son is Nephew; Brother’s/Sister’s daughter is Niece.
• Cousin: Child of one’s uncle or aunt. (Never use “cousin brother” or “cousin sister”).

Example: Pointing to a photograph, a man says, “I have no brother or sister but that man’s father is my father’s son.” Who is in the photograph? Let the man be $M$. $M$ says “my father’s son”. Since $M$ has no brother or sister, “my father’s son” must be $M$ himself. Therefore, “that man’s father is $M$”. So, the man in the photograph is $M$‘s son.

3. Coded Blood Relations

In these problems, relationships are represented by symbols (e.g., $A + B$ means $A$ is the father of $B$).

• Strategy:
  1. Gender Elimination: If you need to find if $P$ is the aunt of $Q$, check the symbol immediately after $P$ to determine if $P$ is female. Eliminate options where $P$ is male.
  2. Generation Gap: Assign numeric values for generation shifts: Parents $= +1$, Siblings $= 0$, Children $= -1$. Sum them up to match the target relationship.

Example: If $P \times Q$ means $P$ is sister of $Q$, and $P + Q$ means $P$ is father of $Q$. Which expression means $A$ is aunt of $B$? For $A$ to be aunt of $B$, $A$ must be female (generation gap $+1$ relative to $B$). Look at $A \times C + B$: $A$ is sister of $C$ ($0$ gap, female), and $C$ is father of $B$ ($+1$ gap). Yes, $A$ is sister of $B$‘s father, i.e., $A$ is $B$‘s aunt.

4. Gender Determination from Clues

• Warning: Never assume a person’s gender from their name (e.g., “Deepak” could be female or male in a logical reasoning puzzle unless specified).
• The last person in a chain of relations (like $A$ is brother of $B$, $B$ is sister of $C$) may have an undetermined gender unless an explicit clue is given.

🌐 Learning Resources

✅ Practice Links

📝 Key Approach

Relationship Map:
  Father's/Mother's son → Brother
  Father's/Mother's daughter → Sister
  Father's brother → Uncle
  Mother's brother → Maternal Uncle
  Father's/Mother's father → Grandfather
  Son's wife → Daughter-in-law

Steps:
  1. Draw a family tree (Males: □, Females: ○)
  2. Use arrows: ↓ = parent-child, — = siblings, = = married
  3. Read the statement from the end to the start

Tip: Words like “only son”, “only daughter”, “only child” are key to narrowing down relationships.

🔗 Related Topics

• Ages — Age clues in family relation puzzles
• Seating Arrangements and Syllogisms — Circular or linear arrangements where seating is determined by blood relations
• Logical Venn Diagrams — Representing subsets of family structures/relations
• Directions and Distance — Tracking coordinate pathways/placements along with relations
• Decision Making and Data Sufficiency — Deciding if statements are sufficient to determine family ties