Construct genealogical family trees, resolve paternal/maternal branches, and decode symbol-based relationship ciphers.
Systematic principles and analytical strategies prescribed by the CBSE curriculum for Blood Relation.
Examine the coded definitions:
• $P + Q$ means P is the father of Q ($Delta G = +1$, Male)
• $P - Q$ means P is the wife of Q ($Delta G = 0$, Female)
• $P \times Q$ means P is the brother of Q ($Delta G = 0$, Male)
• $P \div Q$ means P is the daughter of Q ($Delta G = -1$, Female)
Given the expression: $A + B - C \times D$, how is A related to D?
Decode each segment step-by-step:
Kinship Synthesis:
$A$ is the father of $B$. $B$ is the wife of $C$. Therefore, $A$ is the father-in-law of $C$.
Since $D$ is the sibling of $C$, $A$ is the father-in-law of D's brother.
Final Answer: $A$ is the father-in-law of D's brother (or simply father-in-law of $C$).
Pointing to a gentleman in a photograph, Sunita said: "His mother is the only daughter of my mother."
How is Sunita related to the gentleman in the photograph?
Inside-Out Deconstruction:
Final Answer: Sunita is the Mother of the gentleman.
Printable classroom and self-assessment problem sets for Blood Relations. Covers kinship notation, generational algebra, family tree puzzles, and coded pedigree deduction.
State the generational delta ($Delta G$) and gender requirement for the kinship relation: Maternal Grandmother.
A grandmother belongs to two generations above the reference individual. Maternal specifies the mother's side.
Answer: $Delta G = +2$, Gender: Female.
If it is stated: "A and B are children of C. C is the father of A, but B is not the son of C." What is B to C?
Since $B$ is a biological child of $C$, $B$ must be either a son or a daughter. The statement explicitly rules out that $B$ is the son of $C$. Therefore, $B$ must be the daughter.
Answer: $B$ is the Daughter of $C$.
In English kinship terminology, state the two distinct familial relations designated by the single term Brother-in-law.
The term 'Brother-in-law' encompasses two distinct familial pathways at the same generational level ($Delta G = 0$):
Answer: Spouse's brother OR Sister's husband.
$K$ is the sister of $M$. $M$ is the father of $N$. $N$ is the brother of $P$.
Construct the pedigree tree and determine how K is related to P.
Step-by-Step Tree Construction [1 Mark]:
Kinship Deduction [1 Mark]:
Since $M$ is the father of $P$, and $K$ is the sister of $M$, $K$ is the father's sister of $P$.
Answer: $K$ is the Paternal Aunt (Hindi: Bua) of $P$.
Let $X \$ Y$ denote X is the mother of Y ($Delta G = +1, -$), and $X \# Y$ denote X is the father of Y ($Delta G = +1, +$).
Which of the following expressions establishes that M is the maternal grandmother of T?
(i) $M \$ K \# T$
(ii) $M \$ K \$ T$
(iii) $M \# K \$ T$
Justify your choice using generational delta and gender constraints.
Constraint Analysis [1 Mark]:
Maternal grandmother requires:
1. $M$ must be female ($-$) and two generations above $T$ ($Delta G = +2$).
2. The intermediate parent $K$ must be the mother of $T$ ($Delta G = +1$, Female).
Evaluating Expressions [1 Mark]:
Answer: Expression (ii) $M \$ K \$ T$ correctly establishes that $M$ is the maternal grandmother of $T$.
A family consists of six members: $A, B, C, D, E,$ and $F$. There are two married couples.
1. $B$ is an engineer and the father of $E$.
2. $F$ is the grandfather of $C$ and is a physician.
3. $D$ is the grandmother of $E$ and is a homemaker.
4. There is one engineer, one physician, one teacher, one homemaker, and two students in the family.
5. The teacher is married to the physician.
(i) Identify the two married couples.
(ii) Determine the profession of $A$.
(iii) What is the relationship between $C$ and $E$?
(iv) Identify which two family members are the students.
Step-by-Step Structural Synthesis [2 Marks]:
Answers [2 Marks]:
High-yield summary, generational matrices, pedigree shorthand, and problem-solving shortcuts for Blood Relations in CBSE Class 11 Applied Mathematics.
| Generation ($Delta G$) | Male Members ($[+]$) | Female Members ($[-]$) |
|---|---|---|
| $+2$ (Grandparents) | Paternal Grandfather, Maternal Grandfather | Paternal Grandmother, Maternal Grandmother |
| $+1$ (Parents) | Father, Paternal Uncle (Chacha), Maternal Uncle (Mama), Father-in-law | Mother, Paternal Aunt (Bua), Maternal Aunt (Masi), Mother-in-law |
| $0$ (Self & Siblings) | Self (Male), Brother, Cousin (Male), Husband, Brother-in-law | Self (Female), Sister, Cousin (Female), Wife, Sister-in-law |
| $-1$ (Children) | Son, Nephew (Bhatija / Bhanja), Son-in-law | Daughter, Niece (Bhatiji / Bhanji), Daughter-in-law |
| $-2$ (Grandchildren) | Grandson (Pota / Naati) | Granddaughter (Poti / Naatin) |
Enclose males in square brackets $[+]$ and females in circles or round brackets $[-]$. Never assume gender from a name alone!
Connect married couples with a double horizontal line: $[A] \Leftrightarrow [B]$. One must be male, one female.
Connect brothers and sisters with a single horizontal hyphen at the same level: $A - B$.
Draw vertical lines descending from parents to offspring.
Pointing to a photograph, a woman says: "He is the son of the only son of my grandfather." How is the man in the photograph related to the woman?
$A$'s mother is the sister of $B$ and daughter of $C$. $D$ is the daughter of $B$ and sister of $E$. How is $C$ related to $E$?
If $P + Q$ means $P$ is the husband of $Q$, $P \div Q$ means $P$ is the sister of $Q$, and $P \times Q$ means $P$ is the son of $Q$, what does $A \div B \times C + D$ mean?
Assertion (A): If $X$ is the sibling of $Y$, it cannot be concluded that $Y$ is the brother of $X$.
Reason (R): The gender of $Y$ is not specified; $Y$ could be either a brother or a sister to $X$.
Introducing a man, a woman said: "His wife is the only daughter of my father." How is the man related to the woman? Provide a step-by-step breakdown.
Step 1: Decode the narrator's reference [1 Mark]:
The speaker is a woman. "The only daughter of my father" must be the woman herself (since she is female and her father has only one daughter).
Step 2: Connect to the subject [1 Mark]:
"His wife is [the woman herself]."
Therefore, the man is the husband of the woman.
Answer: The man is the Woman's Husband.
If $P \% Q$ means $P$ is father of $Q$, and $P \star Q$ means $P$ is sister of $Q$, show what relationship is expressed by $M \star N \% T$ between $M$ and $T$.
Segment Analysis [1 Mark]:
$N \% T \implies N$ is the father of $T$ ($Delta G = +1$, Male).
$M \star N \implies M$ is the sister of $N$ ($Delta G = 0$, Female).
Conclusion [1 Mark]:
$M$ is the sister of $T$'s father. Therefore, $M$ is the Paternal Aunt (Hindi: Bua) of $T$.
$A, B, C, D, E,$ and $F$ are six members of a family. The number of males equals the number of females.
1. $A$ and $E$ are sons of $F$.
2. $D$ is the mother of two, one boy and one girl.
3. $B$ is the son of $A$.
Draw the family pedigree tree and identify who the mother of $B$ is.
Pedigree Construction [2 Marks]:
- Total 6 members: 3 males and 3 females.
- $A$ and $E$ are sons of $F \implies A^{(+)}, E^{(+)}$.
- $B$ is the son of $A \implies B^{(+)}$.
- We now have 3 males: $A, E, B$. Since there are only 3 males in total, the remaining 3 members ($F, D, C$) MUST ALL BE FEMALES!
- Thus, $F$ is female (Mother of $A$ and $E$).
- $D$ is a female who is the mother of two children (one boy, one girl). Since $A$ is married with a son $B$, $D$ must be the wife of $A$!
- The daughter of $A$ and $D$ must be $C^{(-)}$.
Kinship Conclusion [1 Mark]:
$D$ is the wife of $A$ and the mother of $B$ and $C$.
Answer: The mother of B is D.
Explain how coded blood relations problems can be verified using the Generational Balance Equation $\sum \Delta G$. Demonstrate with an example.
Methodological Explanation [1.5 Marks]:
Each kinship operator assigns an integer value representing generational shift:
- Parent / Father / Mother: $\Delta G = +1$
- Sibling / Spouse: $\Delta G = 0$
- Child / Son / Daughter: $\Delta G = -1$
Summing $\Delta G$ across an expression from left to right yields the net generational difference between the first and last person. If a relation like 'Grandfather' is queried, the net sum MUST equal $+2$. Any option yielding $\Delta G \neq +2$ can be eliminated instantly without drawing the tree.
Example Demonstration [1.5 Marks]:
For expression $P \xrightarrow{+1} Q \xrightarrow{0} R \xrightarrow{+1} S$, net $\sum \Delta G = 1 + 0 + 1 = +2$. This immediately verifies $P$ is at the grandparent generational level relative to $S$.
Case Background: Legal Inheritance Pedigree Analysis
A civil court is determining the legal heirs of an ancestral property. The family tree records indicate:
1. $P$ is the father of $Q$ and $R$.
2. $Q$ is married to $S$, and they have two children: a son $T$ and a daughter $U$.
3. $R$ is married to $V$, and they have an only daughter $W$.
4. $P$ passes away intestate (without a will).
Q9 (2 Marks): Determine the exact relationship of $T$ to $R$, and $W$ to $Q$.
Q10 (2 Marks): How is $S$ related to $V$, and how is $U$ related to $W$?
Solution to Q9 [2 Marks]:
- $Q$ and $R$ are siblings (children of $P$).
- $T$ is the son of $Q$. Therefore, $T$ is the Nephew of $R$.
- $W$ is the daughter of $R$. Therefore, $W$ is the Niece of $Q$.
Solution to Q10 [2 Marks]:
- $S$ is the wife of $Q$, and $V$ is the spouse of $R$. Since $Q$ and $R$ are siblings, $S$ and $V$ are Co-sisters-in-law (spouses of siblings).
- $U$ is the daughter of $Q$, and $W$ is the daughter of $R$. Since their parents ($Q$ and $R$) are siblings, $U$ and $W$ are first Cousins (Paternal Cousins).