Introduction
Logical Deduction problems give relationships that hold only if certain conditions are true (for example: "If X is male then Y is Z", or "Only if A is the only child..."). These questions test your ability to apply conditional logic (if / only if / unless) to family links and to avoid taking unstated assumptions as facts.
This pattern is important because many exam-style items hide the correct relation behind conditionals - mastering them avoids wrong inferences and ensures precise answers.
Pattern: Logical Deduction (Conditional Relationships)
Pattern
The key idea: Treat each clause as a logical statement (IF, ONLY IF, UNLESS) and determine which relations become true under which conditions; do not apply a relation unless its condition is satisfied.
Typical condition types:
- Conditional (If P → Q): Q holds only when P is true.
- Only if (Q only if P): Q implies P; Q can be true only when P is true.
- Unless / Except: Negation of a condition (treat carefully - often means 'if not').
- Exclusive (only/only child): Forces identity (resolves ambiguity).
Step-by-Step Example
Question
Read carefully:
1) If A is male, then B is A’s son.
2) If A is female, then B is A’s daughter.
3) A is the child of C.
Who is B to C?
(A) Grandson (B) Granddaughter (C) Child (D) Cannot be determined
Solution
-
Step 1: Encode conditions.
Two mutually exclusive conditionals: (A male → B = son of A) and (A female → B = daughter of A). Both describe B as A’s child - gender determines B’s gender but not generation. -
Step 2: Connect generations.
A is child of C → A is one generation below C; B is child of A → B is two generations below C. -
Step 3: Translate to standard relation.
Two generations below → grandchild. Because B’s gender depends on A’s gender, B could be grandson or granddaughter. -
Final Answer:
Cannot be determined → Option D (we know B is C’s grandchild, but gender - grandson vs granddaughter - is conditional and not fixed). -
Quick Check:
B is child of A and A is child of C → B is grandchild of C; if question asked “grandchild” we'd choose it, but options A & B are gendered so DNT is correct. ✅
Quick Variations
1. Conditional + exclusive: "If X is only son of Y, then..." → exclusive resolves identity.
2. Compound conditions: "If P and Q then R" - both must hold to infer R.
3. Negative condition: "Unless A is married, B is the child of C" → treat as "If not married then...".
4. Multiple branches leading to different genders or relations - always map each branch separately then compare.
Trick to Always Use
- Step 1 → Translate every sentence into a logical form (IF P → Q; ONLY IF Q → P; UNLESS → IF NOT P → Q).
- Step 2 → Draw small branched trees for each conditional branch (one tree per scenario) and label relations explicitly.
- Step 3 → Determine which facts are unconditional (apply always) and which are conditional (apply only in the branch where the condition holds).
- Step 4 → If options include gendered terms while the gender is conditional/unknown, prefer a neutral answer (Child/Grandchild) or DNT if neutral option isn't present.
Summary
Summary
- Translate conditional statements into clear logical forms.
- Handle IF, ONLY IF, and UNLESS carefully - each has a different logical direction.
- Draw scenario trees to separate possible cases clearly.
- Prefer neutral or DNT answers when gender or conditionally dependent facts are unclear.
Example to remember:
“If A is male, B is A’s son; if A is female, B is A’s daughter; A is child of C.” → B is grandchild of C (gender not fixed).
Hint: When gender is conditional and both branches possible, pick DNT.
Common Mistakes: Assuming gender of R and forcing a gendered grand-relation.