Blood Relations
🔒 Log in to trackCoded (symbol) relations
🔒 Log in to trackThe Tier-2 favourite: 'P + Q means P is the father of Q; P − Q means P is the mother of Q; ...' Then a coded string like A + B × C must be decoded into a real relation.
Method:
- Rewrite the string as nested statements:
A + B × C= (A is the father of B) and (B is the sister of C). - Build the mini-tree: place A above B; B and C are siblings, so A (the shared parent side) sits above both.
- Read off the asked pair — here A is the father of C.
Gender bookkeeping is the whole game. Each symbol fixes the first person's gender (father → male, mother → female, sister → female). A symbol like 'X is the sibling of Y' fixes nothing. Track genders under the letters as you decode; the answer usually turns on one of them.
Longer strings (A + B × C − D) are the same loop: decode pairwise, extend the tree, read the final pair. Never decode the whole string at once.
Detailed notes
What these questions look like
The exam defines private symbols and hands you a coded string: "'P + Q' means P is the father of Q; 'P × Q' means P is the sister of Q. In 'A + B × C', how is A related to C?" No tree exists yet — you build one from the string. This is the Tier-2 favourite because one well-made string can ask any relation in it.
Decode pairwise, never as a whole
Break the string into symbol-sized sentences, left to right:
A + B→ "A is the father of B."B × C→ "B is the sister of C." Now draw: A above B; B and C share the same parents (sisters do), so A sits above C as well. Read the asked pair: A is C's father. Two operators ≈ three people; three operators ≈ four people. A four-person string likeA + B − C × Dis the same loop one more time.
The gender bookkeeping
Each symbol fixes the gender of its first person only: father/son/brother/husband/uncle → the first person is male; mother/daughter/sister/wife/aunt → female. "Sibling/cousin/child of" symbols fix nothing. So:
- In
A + B × C, A's gender is fixed by "+" (male), B's by "×" (female), C's by nothing. - If the asked relation needs a gender nobody fixed, the answer must be the neutral word ("sibling", "cousin", "parent") or "cannot be determined". Mark +/− under each letter as you decode. The final answer usually turns on exactly one of these marks.
Reading the pair direction
"How is A related to C?" = name A from C's side. Decode A + B as "A is the father of B", but if the question asks "How is B related to A?", the same symbol gives son (or daughter, if B's gender shows female elsewhere). Symbols read left-to-right, questions read either way — always answer the question's direction, not the string's.
Strings where a person appears twice
Longer expressions reuse letters: A + B + C means A is the father of B and B is the father of C, so A is C's grandfather. Chains of the same symbol add generations; chains of different symbols mix a generation step with a sideways step. Draw the tree — do not try to feel the answer.
Quick revision
- Decode one symbol at a time; each symbol = one sentence = one tree link.
- A symbol fixes the first person's gender only; blanks stay blank.
- Parent of one sibling is parent of all siblings.
- Same symbol twice = +1 generation (father → grandfather).
- Answer in the question's direction; use neutral words for blank genders.
- Check the tree before marking: no person can be their own ancestor.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Three-person decode (two symbols)very common3 practice Q
Two symbol definitions and a string like 'A + B × C'; one pair's relation is asked.
- Translate each symbol into a plain sentence.
- Draw the mini-tree: shared parents for siblings, marriage on one row.
- Read the asked pair from the tree, watching which genders the symbols fixed.
Why it works: two sentences already form a connected tree; the answer is one path on it.
Example: 'P + Q' means P is the brother of Q; 'P × Q' means P is the wife of Q. In 'A + B × C', how is A related to C?
A is B's brother; B is C's wife. Husband's brother → A is C's brother-in-law.
Type 2: Four-person string (three symbols)common2 practice Q
Three symbol definitions; the string has three operators, e.g. 'A + B − C × D'.
- Decode symbol by symbol, left to right, drawing as you go.
- Each operator adds one person; link siblings under shared parents.
- Answer the asked pair; a gender no symbol fixed means a neutral word.
Why it works: the string is just three sentences; three small links beat one long guess.
Example: 'P + Q' = P is the son of Q; 'P − Q' = P is the wife of Q; 'P × Q' = P is the brother of Q. In 'A + B − C × D', how is A related to D?
A is B's son; B is C's wife → C is A's father; C is D's brother → A is D's nephew (A is male).
Type 3: Reverse-direction ask in coded stringscommon2 practice Q
The question asks 'How is C related to A?' while the string runs A ... B ... C.
- Decode and draw exactly as usual — do not reverse the string.
- Take the viewpoint the question names (C's side).
- Give the mirror word of what the path shows.
Why it works: the tree is direction-free; only the final sentence must match the question's direction.
Example: 'X # Y' means X is the father of Y; 'X @ Y' means X is the sister of Y. In 'A # B @ C', how is C related to A?
A is B's father; B is C's sister → A is C's father too. Asked from C's side: C is A's son or daughter — C's gender is never fixed → 'cannot be determined' unless a neutral option exists.
Type 4: Build the expression for a given relationoccasional3 practice Q
'Which expression means M is the maternal uncle of K?' — options are strings, not words.
- Write the target as plain sentences ('M is the brother of K's mother').
- Pick symbols that state exactly those sentences, middle person included.
- Check every option symbol by symbol; reject any that changes a gender or a generation.
Why it works: each option is one claimed tree; the correct one must reproduce the target sentences exactly.
Example: 'P + Q' = P is the brother of Q; 'P − Q' = P is the mother of Q. Which expression means 'M is the maternal uncle of K'?
Need: M is the brother of K's mother. 'M + L − K' says M is L's brother and L is K's mother ✓ → M + L − K.
Shortcut tricks
⚡ Decode pairwise, tree under it
For each operator, write its one-line sentence beneath the string, then draw the tree. Two operators ≈ four people; three ≈ five.
Example: Q. 'X % Y' = X is the wife of Y; 'X # Y' = X is the sister of Y. In M % N # O, how is M related to O?
Sol. M is the wife of N; N is the sister of O. M is the wife of O's sister → sister-in-law.
Pairwise decoding turns a 6-symbol string into 3 plain sentences.
⚡ Gender audit before answering
Before marking, check every needed gender is pinned by a symbol. If the asked relation needs a gender nobody fixed, the answer is the gender-neutral form (cousin, sibling-in-law phrasing) — or you have mis-decoded.
Example: Q. 'P @ Q' = P is the son of Q; 'P & Q' = P is the husband of Q. In P @ Q & R, how is R related to P?
Sol. P is the son of Q; Q is the husband of R. R is Q's wife, Q is P's parent → R is P's mother.
Q's male gender (husband) is what converts 'parent of P' into 'mother'.
Where students lose marks
Decoding
A + B × Cas 'A is the father of C' and forgetting to verify the sibling link connects the right pair.Assuming the gender of a person whose operator fixes none (e.g. 'brother of Y' fixes the first, not Y).
Reading the final question in the reverse direction (M↔O mix-ups).
Practice sets — 13 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 13 questions
Suggested time 10 min · wrong answers go to your mistake notebook automatically.