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Logical Deduction (Conditional Relationships)

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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: Logical Deduction (Conditional Relationships)

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

  1. 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.

  2. 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.

  3. 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.

  4. Final Answer:

    Cannot be determined → Option D (we know B is C’s grandchild, but gender - grandson vs granddaughter - is conditional and not fixed).

  5. 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

  • 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).

Practice

(1/5)
1. Read carefully:

1) If R is male, then S is R’s son.
2) If R is female, then S is R’s daughter.
3) R is the child of T.

Who is S to T?

(A) Grandson (B) Granddaughter (C) Child (D) Cannot be determined
easy
A. Grandson
B. Granddaughter
C. Child
D. Cannot be determined

Solution

  1. Step 1: Analyze the conditions.

    If R is male → S is son of R. If R is female → S is daughter of R. Both make S a child of R, but gender changes.

  2. Step 2: Connect with T.

    R is child of T → S is grandchild of T, but gender of S is unknown.

  3. Step 3: Conclude.

    Gender ambiguity makes both Grandson and Granddaughter possible → choose D (Cannot be determined).

  4. Final Answer:

    Cannot be determined → Option D.

  5. Quick Check:

    Two generations down, gender unknown → DNT ✅
Hint: When gender is conditional and both branches possible, pick DNT.
Common Mistakes: Assuming gender of R and forcing a gendered grand-relation.
2. Read carefully:

1) If X is the only son of Y, then Z is the son of X.
2) X is the only son of Y.

How is Z related to Y?

(A) Grandson (B) Granddaughter (C) Son (D) Cannot be determined
easy
A. Grandson
B. Granddaughter
C. Son
D. Cannot be determined

Solution

  1. Step 1: Apply the conditional.

    Given: If X is the only son of Y → Z is the son of X. We're told X is the only son of Y, so the condition holds.

  2. Step 2: Trace generations.

    Z is son of X, and X is son of Y → Z is a male grandchild of Y (grandson).

  3. Final Answer:

    Grandson → Option A.

  4. Quick Check:

    Son of your son = grandson ✅
Hint: An 'only son' clause fixes identity; follow the chain down one generation to get 'grand-'.
Common Mistakes: Mistaking Z for Y’s son (skipping one generation).
3. Read carefully:

1) If M is male then N is M’s son.
2) If M is female then N is M’s daughter.
3) M is male and M is the child of P.

Who is N to P?

(A) Grandson (B) Granddaughter (C) Child (D) Cannot be determined
easy
A. Grandson
B. Granddaughter
C. Child
D. Cannot be determined

Solution

  1. Step 1: Use the given branch.

    M is male → by (1) N is M’s son (male child of M).

  2. Step 2: Connect generations.

    M is child of P → N is child of M → N is two generations below P → a grandchild. Because N is explicitly male, he is a grandson.

  3. Final Answer:

    Grandson → Option A.

  4. Quick Check:

    M (child of P) → N (son of M) → N is P’s grandson ✅
Hint: When a conditional branch explicitly fixes gender, you can pick the gendered grand-relation directly.
Common Mistakes: Ignoring the given branch (M is male) and selecting DNT.
4. Read carefully:

1) If A is the only daughter of B, then C is A’s mother.
2) A is the only daughter of B.

How is C related to A?

(A) Father (B) Mother (C) Aunt (D) Cannot be determined
medium
A. Father
B. Mother
C. Aunt
D. Cannot be determined

Solution

  1. Step 1: Apply the conditional.

    Given: If A is the only daughter of B → C is A’s mother. We are told A is the only daughter of B, so the condition is satisfied.

  2. Step 2: Direct inference.

    Therefore C is A’s mother.

  3. Final Answer:

    Mother → Option B.

  4. Quick Check:

    Condition true → consequence holds (C = mother) ✅
Hint: When a conditional and its antecedent are both given true, accept the consequent as fact.
Common Mistakes: Confusing 'only' with 'only if' - read wording carefully.
5. Read carefully:

1) If X’s father is the only son of Y, then Z is sibling of X.
2) X’s father is the only son of Y.

How is Z related to Y?

(A) Son (B) Daughter (C) Grandchild (D) Cannot be determined
medium
A. Son
B. Daughter
C. Grandchild
D. Cannot be determined

Solution

  1. Step 1: Apply the conditional.

    X’s father is the only son of Y → by (1), Z is sibling of X.

  2. Step 2: Trace generations.

    X and Z being siblings means both are children of X’s father. X’s father is son of Y → X and Z are grandchildren of Y.

  3. Final Answer:

    Grandchild → Option C.

  4. Quick Check:

    Child of Y’s son = grandchild of Y ✅
Hint: Translate 'father is Y’s son' → children of father become Y’s grandchildren.
Common Mistakes: Mistaking sibling-of-X for child-of-Y directly (skip generation).