Coded Relationship
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Logical Framework
Study MaterialLogical Framework for Coded Relationship
Logical Framework is a systematic approach to solving Coded Relationship questions quickly and accurately. Instead of decoding every relationship from the beginning, candidates can follow a fixed sequence of logical checks to eliminate incorrect options and identify the correct relationship.
Coded Relationship questions may contain several symbols representing relationships such as father, mother, brother, sister, husband, wife, son, and daughter. The coding may also be given in either forward type or backward type.
A proper logical framework helps reduce unnecessary calculations and avoids spending time on answer choices that can be rejected immediately.
Key Observation:
The fastest way to solve a Coded Relationship question is to eliminate impossible options first and perform detailed relationship analysis only for the options that remain.
What is the Logical Framework?
The Logical Framework is a step-by-step method used to analyse coded relationships without immediately constructing a complete family tree for every option.
The framework mainly consists of the following stages:
- Understand the coding system.
- Identify the coding direction.
- Identify the person whose relationship is being asked.
- Check the required sex.
- Check the generation gap.
- Eliminate impossible choices.
- Draw a family tree for the remaining choices.
- Determine the exact relationship.
Core Principle:
Eliminate first, analyse later. If an option violates the required sex or generation gap, there is no need to decode the complete relationship.
Step 1: Understand the Coding System
The first step is to carefully read the meanings of all symbols given in the question.
For example, a question may state:
A + B means A is the father of B.
A - B means A is the mother of B.
A x B means A is the brother of B.
A ÷ B means A is the sister of B.
Do not assume that a symbol always has the same meaning across different questions. The meanings must always be taken from the information provided in that particular question.
Important Rule:
Always decode the symbols according to the coding system given in the question. Never apply the coding system from another question.
Step 2: Identify the Coding Direction
After understanding the symbols, determine whether the question uses forward-type or backward-type coding.
| Coding Type | Basic Rule | Direction |
|---|---|---|
| Forward Type | The first person has the given relationship with the second person. | Normally left to right |
| Backward Type | The second person has the given relationship with the first person. | Normally right to left |
Forward Type
In forward-type coding, the first person is the subject of the stated relationship.
For example:
A + B → A is the father of B
Backward Type
In backward-type coding, the second person is the subject of the stated relationship.
For example:
A ^ B → B is the father of A
Mind It!
The direction of coding is extremely important. A relationship that looks similar may represent completely different relationships depending on whether the coding is forward or backward.
Step 3: Identify the Person in Question
Read the question carefully and identify exactly which person's relationship must be determined.
For example:
"Which of the following means that A is the grandmother of B?"
Here, the person under consideration is A.
Therefore, the first checks should focus on whether A can be female and whether A can be two generations above B.
Similarly, if the question asks:
"Which of the following means that X is the grandson of Y?"
the person under consideration is X.
Step 4: Check the Sex
Once the person under consideration is identified, determine whether that person must be male or female.
| Relationship | Required Sex |
|---|---|
| Father | Male |
| Grandfather | Male |
| Brother | Male |
| Son | Male |
| Mother | Female |
| Grandmother | Female |
| Sister | Female |
| Daughter | Female |
For example, if the question asks whether A is the grandmother of B, A must be female.
If an option immediately establishes that A is the father or brother of another person, A is male and that option can be rejected.
Shortcut:
If the first relationship connected to the person under consideration establishes the wrong sex, eliminate the option immediately.
Forward-Type Sex Checking
In forward-type coding, examine the symbol immediately after the person under consideration.
For example, if A is the person in question and the option begins with:
A + B
If + means father, then A is male.
Therefore, if the question requires A to be female, the option can be eliminated without further analysis.
Backward-Type Sex Checking
In backward-type coding, examine the symbol immediately before the person under consideration.
For example, if B is the person in question and an option contains:
A < B
If < means B is the daughter of A, B is female.
Therefore, if B is required to be male, the option can immediately be rejected.
Quick Rule:
Forward coding: Check immediately after the person.
Backward coding: Check immediately before the person.
Step 5: Check the Generation Gap
After checking sex, the next step is to determine whether the required generation gap is possible.
The generation gap tells us how many generations one person is above or below another.
| Relationship | Generation Gap |
|---|---|
| Father / Mother | +1 |
| Brother / Sister | 0 |
| Husband / Wife | 0 |
| Son / Daughter | -1 |
Therefore:
- Father or mother contributes +1.
- Brother or sister contributes 0.
- Husband or wife contributes 0.
- Son or daughter contributes -1.
Generation Gap Examples
Grandfather Relationship
If A is the grandfather of B, A is two generations above B.
Generation Gap = +2
Grandson Relationship
If X is the grandson of Y, X is two generations below Y.
Generation Gap = -2
Brother Relationship
Brothers belong to the same generation.
Generation Gap = 0
Uncle Relationship
An uncle is normally one generation above his nephew or niece.
Generation Gap = +1
Step 6: Calculate the Generation Gap
To calculate the generation gap, consider only the symbols between the two persons under consideration.
Calculation Method
- Identify the two persons.
- Identify the direction of coding.
- Move through the relevant symbols.
- Assign the appropriate generation value to each relationship.
- Add the values.
- Compare the result with the required relationship.
For example:
A + B + C
A is the father of B and B is the father of C.
Gap = +1 + +1 = +2
Therefore, A is the grandfather of C.
Similarly:
A x B + C
A is the brother of B and B is the father of C.
Gap = 0 + +1 = +1
Therefore, A is of C's father's generation.
Step 7: Ignore Zero-Value Relationships
When calculating the generation gap, brother, sister, husband, and wife relationships contribute 0.
Therefore, they do not change the numerical generation gap.
Time-Saving Tip:
In many examination questions, you can ignore all brother, sister, husband, and wife relationships while calculating the generation gap. Focus mainly on father/mother and son/daughter relationships.
Step 8: Eliminate Impossible Choices
After checking sex and generation gap, eliminate all options that fail either condition.
For example, suppose the question asks:
"Which of the following means A is the grandmother of B?"
Then:
- A must be female.
- A must be two generations above B.
Any option that makes A male can be rejected immediately.
Any remaining option that does not produce a generation gap of +2 can also be rejected.
Mind It!
Do not draw a complete family tree for an option that has already failed the sex or generation-gap test.
Step 9: Draw a Family Tree for Remaining Choices
If two or more options remain after the quick elimination process, construct a family tree for those choices.
A family tree gives a visual representation of the relationships and helps determine the exact relationship.
Basic Family Tree Rules
- Use vertical or diagonal lines for parent-child relationships.
- Use a double horizontal line for marriage relationships.
- Use a dashed line for brother or sister relationships.
- Use + for a male person.
- Use - for a female person.
- Use ? when the sex or identity is unknown.
Key Observation:
The family tree should normally be the final verification step, not the first step. Quick elimination can often remove several incorrect choices before any diagram is required.
Complete Logical Framework
The entire solving process can be summarized as follows:
Read the Coding Information
↓
Identify Forward / Backward Type
↓
Identify the Person in Question
↓
Check Required Sex
↓
Check Generation Gap
↓
Eliminate Wrong Choices
↓
Draw Family Tree for Remaining Choices
↓
Determine Exact Relationship
↓
Select the Correct Answer
Integrated Example
Suppose a question asks:
Which of the following means that A is the grandfather of B?
Use the logical framework instead of completely decoding every option.
Step 1: Identify the Person
The person under consideration is A.
Step 2: Check Sex
A grandfather must be male.
Therefore, eliminate every option in which A is immediately identified as a mother, sister, wife, or daughter.
Step 3: Check Generation Gap
A grandfather is two generations above B.
Therefore:
Required Generation Gap = +2
Step 4: Eliminate More Choices
Reject any remaining option whose generation gap is not +2.
Step 5: Draw the Family Tree
If more than one option still remains, draw a family tree and determine the exact relationship between A and B.
Step 6: Select the Answer
The option that satisfies both the sex requirement and the generation-gap requirement, and gives the required relationship in the family tree, is the correct answer.
Forward vs Backward Logical Approach
| Feature | Forward Type | Backward Type |
|---|---|---|
| Relationship Direction | First person → Second person | Second person → First person |
| Normal Reading Direction | Left to right | Right to left |
| Sex Check | Symbol immediately after person | Symbol immediately before person |
| Generation Gap | Move from left to right | Start from right and move left |
| Family Tree | Use after elimination | Use after elimination |
Common Mistakes to Avoid
- Assuming that a symbol always has the same meaning.
- Ignoring whether the coding is forward or backward.
- Checking the wrong side of the person during sex elimination.
- Decoding every option completely from the beginning.
- Ignoring the generation gap.
- Counting brother, sister, husband, or wife as a generation change.
- Drawing a family tree for every option unnecessarily.
- Forgetting that reversing the direction changes the interpretation.
- Selecting an option without verifying the final relationship.
Exam Strategy
In an examination, speed is important. The following sequence is generally more efficient than solving every option completely.
| Priority | Action | Reason |
|---|---|---|
| 1 | Read the coding rules | Understand the symbols |
| 2 | Identify coding direction | Avoid reversing relationships |
| 3 | Identify the person asked about | Focus the analysis |
| 4 | Check sex | Quickly eliminate impossible choices |
| 5 | Check generation gap | Eliminate structurally impossible choices |
| 6 | Draw family tree | Resolve the remaining choices |
| 7 | Verify the relationship | Avoid final mistakes |
Quick Revision Checklist
- Have I read the meaning of every symbol?
- Is the coding forward or backward?
- Which person is being asked about?
- What sex must that person have?
- Does the immediate symbol confirm the correct sex?
- What generation gap is required?
- Have I ignored the zero-generation relationships?
- Can any options be eliminated immediately?
- Do I need to draw a family tree?
- Does the final option actually give the required relationship?
Quick Learning Framework
Understand the Codes
↓
Identify Coding Direction
↓
Find the Person in Question
↓
Check Sex
↓
Check Generation Gap
↓
Eliminate Wrong Options
↓
Draw Family Tree
↓
Verify Relationship
↓
Choose the Answer
Final Takeaway
The Logical Framework for Coded Relationship provides a systematic way to solve relationship-coding questions without wasting time on unnecessary calculations.
The most important principle is to eliminate wrong choices before solving the complete relationship. First understand the coding system and identify whether it is forward or backward. Then identify the person under consideration and check the required sex.
Next, calculate the generation gap using +1 for father or mother, 0 for brother, sister, husband, or wife, and -1 for son or daughter. Once the impossible options are removed, use a family tree to resolve the remaining choices.
With regular practice, this framework helps candidates solve Coded Relationship questions faster, avoid common mistakes, and improve accuracy in competitive examinations.