## SBI PO level Reasoning Family Relation problems can also be solved quickly by Collapsed Column Technique

We have discussed logic analysis in our earlier sessions on * Simple logic analysis*,

*and efficient method of collapsed column logic analysis technique for solving SBI PO or higher level logic puzzles in our previous sessions on*

**Complex logic analysis***and*

**How to solve SBI PO level logic puzzles in a few simple steps 1**

**How to solve SBI PO level logic puzzles in a few simple steps 2.**In this session * we will expand the scope of the powerful method* further through solving a series of SBI PO level Reasoning problems on family relations with characteristic ease.

Before going through this session, you are urged to go through the above-mentioned **first and second session on efficient solution process for logic puzzles.**

### Warning:

The * collapsed column logic analysis technique* may seem to be easy and attractive for solving logic puzzles of any difficulty level efficiently in quick time. But these problems are inherently confusing and potentially a mine-field of errors.

**Unless** the problem solver

**understands the nature and structural variation**of this problem class,**absorbs**the efficient collapsed column technique with sufficient clarity and- builds up confidence through the
**essential activity**of solving many such problems of different structures,

attempting such a tricky logic puzzle **in actual test environment is not recommended.** There is nothing wrong with the method, but large puzzles being inherently complex and confusing, chances of losing your way wasting critically valuable time will be high.

We will take up a series of SBI PO level reasoning problems on family relations now for efficient solutions using * Collapsed column logic analysis technique* that

*simplifies the solution process and reduces the time to solve considerably.*

### Assignment logic analysis using Collapsed column logic analysis technique can be applied to a number of Reasoning problem types

In * Assignment logic analysis problems* there is a set of objects that are to be assigned (or mapped) to a second set of objects determined by a set of logic statements or conditions.

The objects that are to be assigned belong to the to-be-assigned object set (TBA object set) and the objects to which the to-be-assigned objects are to be assigned belong to the to-be-assigned-to object set (or TBAT object set). * In case of one-to-one unique assignment* between two object sets, any of the two object sets are interchangeable with the other with respect to assignment as an assignment between two objects is a mutual two directional operation.

In the simplest form of assignment logic analysis problem, one set of objects are to be assigned to a second set of objects according to a third set of given conditions. The conventional method to solve this form of problems is to represent the values of the two object sets, one as rows and the second as columns. **This representation is the simplest form of 2 dimensional logic table.**

The cell values represent assignment between the members of the two sets. For example one set may be husbands and the second wives; problem will be to determine who is married to whom according to a set of conditions. The names of husbands may form row labels and names of wives column labels. Cross section of a row and column will represent marital status of the pair involved.

Commonly we encounter logic analysis problems of assignment type in * logic puzzles* which occasionally seem to be quite confusing. We have already used the efficient technique of collapsed logic table columns in solving logic puzzles in our earlier sessions. Now we will apply the same technique to solve a different category of Reasoning problems, namely

*problems. In future sessions we will show how the same method can be applied for efficient solution of*

**Reasoning Family Relation***and*

**Floor type***as well.*

**Sitting arrangement type of Reasoning problems**Use of same concept and similar method in solving varieties of Reasoning problems eases the overall problem of solving a large portion of difficult reasoning problems considerably.

Usually the subcategory of Family relation problems is referred to as * Blood relation problems* which is nothing but a subset of Family relation problems.

*Blood related family is always a subset of extended family in real life.*

### Stages in Reasoning logic analysis problems

One of the most important stages in solving reasoning logic analysis problems of any type is the * first stage* of

*Unless such a problem is represented in appropriate efficient form, attempt to solve the problem in any which way most possibly ends up in confusion.*

**Problem structure analysis and representation.**For example, in our earlier logic puzzle solution we have identified its nature as an * assignment type logic puzzle problem* and used the final collapsed column logic table of the form,

In the * second stage, we Analyze logic statements in conjunction with the problem state* to determine the sequence of executing or processing the logic statements. Any logic problem will have a prime component in the form of a set of logic or condition statements.

*On an appropriate problem representation*

**In second stage we determine the efficient sequence of executing the conditional statements.**

**if we can apply an efficient sequence of execution of logic conditions, often the problem is solved much faster.**In the * third repetitive stage we actually carry out analysis and execution of one or more than one logic statement at each step.* This is the last level and

*With proper execution of the individual logic statements coupled with proper sequencing or selection of logic statements for execution, the problem logic table can be simplified greatly at a single step.*

**forms the core of elementary logic analysis.**At this stage the * clarity in domain knowledge plays a critical role.* For example, in the process of solving a reasoning problem on family relations,

**you must be very clear about the commonly accepted form of relations between various members of a common family.**### Family relation logic problems

The following is a snapshot of commonly accepted relations between various members of a family. This in fact is a network of relations with every node connected to every other node signifying a specific relation. Technically, a family is a fully connected graph with each node connected to all the other nodes.

Though every node has a connected edge from every other node, we have not shown a number of connections to keep the picture uncluttered. An important point to note in family relation network is the nature of relationships between any two members in a family. Any such relation can be described in two different ways depending on which member is mentioned first in the relation statement.

* For example,* for the married couple [c-a], the woman [a] is wife of the man [c] while the man [c] is the husband of the woman [a]. Thus "husband" is the attribute or role of [c] while "wife" is the role of [a] in this single relationship. Consequently the relationship is represented as a bi-directional arrow.

Same holds good for any other relationship between two members of a family.

### Problem example 1: Reasoning Family Relation problem 1: What are the relationships between the members of the family?

#### Problem description

There are five persons, A, B, C, D, and E of a family.

#### Conditional statements

- B is unmarried and also A's daughter.
- E is C's brother.
- C is the only husband of a married couple in this family.
- A is father of two sons and a daughter. He also has a daughter-in-law.

#### Questions

**Question 1-1.** Who is D's husband?

- E
- C
- A
- Data insufficient
- None of the above

**Question 1-2.** Which of the following statements is definitely correct?

- D is sister-in-law of C
- C is married to B
- D is the daugher of A
- B is the daughter-in-law of A
- D is sister-in-law of E

**Question 1-3.** Which of the following statements is definitely wrong?

- A is a father-in-law
- C's wife is D
- B has a sister-in-law
- D is daughter-in-law of A
- C is E's brother-in-law

**Question 1-4.** Who is D's father-in-law?

- E
- C
- A
- Data insufficient
- None of the above

**Question 1-5.** Who is the brother of D?

- C
- E
- A
- Data insufficient
- None of the above

#### Problem example 1: Solution to the family relation reasoning problem 1: Problem analysis

Note that there is only one object set of 5 family members. The * set of relationships are not physical objects.* Instead

*, that is, two family members. This characteristic of family relationships is true for most types of relationships.*

**these are binary attributes involving a pair of objects**Another specialty of a relationship is, there are always ** two roles involved in a relationship**,

*one each for each member involved in the relationship*. For example, in the case of a married couple, "wife" is the role or attribute of the woman while "husband" is the role of the man.

But then what is to be assigned? The answer in this case is simple. Inevitably the only physical set of family members will form the set of objects to-be-assigned-to and will represent the row labels in the collapsed column logic table (effectively a member of same set is assigned to another member and the assignment is represented by a specific bi-directional relationship, but this might seem to be confusing).

As soon as we are able to assign a specific relationship role to a family member with respect to a second family member, the role of the second member with respect to the first is also determined automatically (from the * family relation concept network*).

#### Solution Strategy

As usual * we will first execute those conditional statements that directly define a relation between two members*, and

*next we will process the statements bearing largest amount of information.*

**Solution steps**

**Step 1.** According to our efficient strategy we will execute Statements 1 and 2 sequentially but together in the first step as both these statements specify definitive relationships between two members. Following is the result problem state in this step,

Note that as soon as we encounter one statement assigning a role to a member such as "E is C's brother", we create two entries against row for E and also against the row for C.

In this problem we have kept * two cells for each row label and the single assignment column* for recording relation statements and analysis results. For larger problems we may need to use more number of cells per row-column intersection. In this first step, we have used both the cells for row B to keep things clear. We could have though combined the two conditions using one cell only. It always is a better practice to record one result in one cell (

*).*

**in actual exam, these cells will be just white space left between rows conveniently****Step 2.** Out of the two statements left, we find the statement 4 to contain largest amount of information. In fact it clearly indicates that A is the head of the family having 2 sons and 1 daughter with 1 son married. * Obviously the 5th member will be the daughter-in-law.* Let us see the problem state after processing statement 4 in this second step.

As expected, we just have recorded in this step that A has 2 sons one of whom is married.

**Note:** At this stage itself you can identify C and E as the two sons of A and D as the daughter-in-law.

**Logic chain:** E is one son (being brother, the only identified male at this point), C or D is the other > if D is the other son then C becomes the fourth child of A violating given condition > C must be the second son and D the daughter-in-law, but you won't know who the husband of D is.

**Step 3.** With this problem state when we process the last statement 3, "C is the only husband of a married couple in this family.", automatically C is identified as the only son of A who is married. As E is C's brother, E becomes the second son of A. Now the only member left to be identified is D and she automatically is identified as the daughter-in-law of A and hence wife of C. This is what we call the * third stage of logic analysis in the domain of family relationship concepts.* Without clarity of family relationship concepts successful execution of this step may not be possible for a complex problem on family relationships.

The final fully assigned logic table will be,

Now we are ready to answer the questions and it should take only about a minute's time to answer the five questions.

#### Answers

**Question 1-1.** Who is D's husband?

Answer 1-1. Option 2: C.

**Question 1-2.** Which of the following statements is definitely correct?

Answer 1-2. Option 5: D is sister-in-law of E.

**Note:** You should be clear about the two-way relationship concept and the fully enumerated family relation network for answering this type of question with speed and accuracy.

**Question 1-3.** Which of the following statements is definitely wrong?

Answer 1-3. Option 5: C is E's brother-in-law

**Question 1-4.** Who is D's father-in-law?

Answer 1-4. Option 3: A.

**Question 1-5.** Who is the brother of D?

Answer 1-5. Option 4: Data insufficient.

**Note:** * About Option values "Data insufficient" and "None of the above":* According to the problem nothing is mentioned about D, the daughter-in-law. She might have a brother who is not mentioned, or in other words, which information is not included (or negated) in the given Data. That's why the answer is Option 4: Data insufficient. On the other hand, if the Option 4 value were "B", the answer would have been "None of the above". In the given problem, as "Data insufficient" becomes a correct choice, the fifth option of "None of the above" violates this fourth option value, and hence is incorrect.

This is a simple problem on family relationships only, though **the framework used may very well cater to efficient solution of any complex problem on purely family relationships, however large the number of members be.**

Next we will explain the solution process of * a similar problem on family relationships* but

*This forms a second object set along with the family members and we will use the*

**with an additional complexity of Professions of family members.***for this problem. Solution process will again be through the same method using one collapsed column and five rows with compound row-column intersection cells.*

**professions as the to-be-assigned-to row labels**### Problem example 2: Reasoning Family Relation problem 2: What are the professions and relationships between the members of the family?

#### Problem description

There are five persons, A, B, C, D, and E of a family. They are by profession, a businessman, a lawyer, a teacher, a farmer and a doctor but not necessarily in the same order.

#### Conditional statements

- B is an unmarried teacher and also A's daughter.
- E is a lawyer and C's brother.
- C is the only husband of a married couple in this family.
- A is a farmer, father of two sons and a daughter.
- A's daughter-in-law is a doctor.

#### Questions

**Question 2-1.** Who is C's brother and what is his profession?

- B; Teacher
- D; Farmer
- A; Businessman
- E; Lawyer
- Data insufficient

**Question 2-2.** Who is the businessman in the family?

- E
- C
- D
- B
- None of the above

**Question 2-3.** Who is E's wife and what is her profession?

- D; Doctor
- B; Teacher
- C; Doctor
- Data insufficient
- None of the above

**Question 2-4.** Which of the statement below is definitely wrong?

- A is head of the family
- D is a single child
- C is a businessman
- C is B's sister
- D's father-in-law is A

**Question 2-5.** Who is the doctor in the family?

- C
- D
- E
- Data insufficient
- None of the above

#### Problem example 2: Solution to the family relation reasoning problem 2: Problem analysis

In addition to the special assignment requirement for binary attribute of family relation, we have a specific object set of family members to be assigned to the row labels corresponding to the five professions. The same single collapsed column representation will be used for recording the results of analysis and statement execution. Only, instead of using 2 cells for each row label, we will use 3 cells-just a little more extra space, to record the family members' identifications.

#### Solution Strategy

As usual * we will first execute those conditional statements that directly define an assignment between a family member and a profession*, and

*next we will process the statements bearing largest amount of information.*

**Solution steps**

**Step 1.** According to our efficient strategy we will execute Statements 1, 2 and 4 sequentially but together in the first step as only these statements make * specific assignment of a member to a profession.* Mark that

*. Following is the result problem state in this step,*

**relationship takes secondary precedence here****Step 2.** In the second step, we will process both the remaining two statements 3 and 5 to create full assignment of the logic table. Let us show the final logic table state first and then will explain the logic behind these last stage assignments.

C being the only husband of a married couple and A having a daughter-in-law, the definitive implication is, C is a son of A and is married. **This is logic analysis in family relations domain.**

As E is C's brother, E is identified as the second son of A. The person left is D (B has already been identified as the daughter of A, the head of the family) and so D must be the doctor, wife of C and daughter-in-law of A.

The remaining unassigned profession of businessman goes to C because from the problem description it follows that every member has a separate profession.

As before, after forming the final logic table, answering the five questions should take about only a minute more.

#### Answers

**Question 2-1.** Who is C's brother and what is his profession?

Answer 2-1. Option 4: E; Lawyer.

**Question 2-2.** Who is the businessman in the family?

Answer 2-2. Option 2: C.

**Question 2-3.** Who is E's wife and what is her profession?

Answer 2-3. Option 5: None of the above.

**Note: **As per the problem description, C is the only married son of A. So the other son E is unmarried and thus the question of his wife does not arise. All the first four choice values are thus incorrect and this implies, the fifth choice value "None of the above" is the correct choice.

**Question 2-4.** Which of the statement below is definitely wrong?

Answer 2-4. Option 4: C is B's sister.

**Note:** You need to be alert while answering this type of question. Consider the choice 2: "D is a single child". * You can't say for sure that* the statement is incorrect as no further information about D, the daughter-in-law, is supplied in the problem description, she might very well be a single child..

**Question 2-5.** Who is the doctor in the family?

Answer 2-5. Option 2: D.

These problems are solvable by * single collapsed column logic tables* as these involve

*However complex the logic conditions are, if the assignments are unique one-to-one, with judicious sequencing of statement execution and suitable third stage logic analysis, such a problem is always solvable with ease, assurance and efficiency.*

**one-to-one unique assignments.**Now * we increase the complexity* by destroying the one-to-one assignment condition. In such an assignment problem, number of objects in a to-be-assigned set is more than the number of objects in a to-be-assigned-to set creating the

*For example if we increase the number of family members to 7 keeping the professions numbering still 5,*

**complexity of one-to-many assignment condition.**

**there is bound to be at least one profession corresponding to more than one family member (for 1 profession having more than one family member, the number of members having this profession will be 3 in this case).**### Problem example 3: Reasoning Family Relation problem 3: What are the professions and relationships between the members of the family?

#### Problem description

There are seven persons, A, B, C, D, E, F and G in a family. Their individual professions are one of businessman, lawyer, teacher, farmer and doctor (not necessarily in the same order). At most two family members may have the same profession and each profession will have at least one family member.

#### Conditional statements

- B is an unmarried teacher and also A's daughter.
- G's sister is a teacher.
- A is a farmer, father of two sons and a daughter.
- A's daughter-in-law, an only child, is a doctor.
- F's sister and her husband both are farmers.
- E is a lawyer and C's brother.

#### Questions

**Question 3-1.** Who is C's sister?

- F
- G
- B
- Data insufficient
- None of the above

**Question 3-2.** What is G's profession?

- Businessman
- Doctor
- Teacher
- Farmer
- None of the above

**Question 3-3.** Who is F's husband?

- A
- C
- E
- Data insufficient
- None of the above

**Question 3-4.** Which of the statements below is definitely wrong?

- A is head of the family
- C's profession is businessman
- C is F's sister
- F is G's sister
- D's father-in-law is A

**Question 3-5.** Which of the statements below is definitely correct?

- F's son is a lawyer
- E's wife is a doctor
- D's mother is a teacher
- G is a mother
- E is D's sister-in-law

#### Problem example 3: Solution to the family relation reasoning problem 3: Problem analysis

Out of the two object sets Family members and Professions, the second having less number of objects than the first, it will be used as the to-be-assigned-to object set to which the larger number of family members will be assigned. The relationship analysis will be carried out simultaneously with profession assignment analysis.

With the condition: "At most two family members may have the same profession and each profession will have at least one family member", the number of collapsed columns will be two and number of professions with more than one family member will also be 2 and the rest 3 professions with 1 family member).

The five professions will form five compound rows.

To record assigned family member name and the relation analysis results, we will use three cells for each row-column intersection pair.

#### Solution Strategy

As usual * we will first execute those conditional statements that directly define an assignment between a family member and a profession*, and

*next we will process the statements bearing largest amount of information.*

**Solution steps**

**Step 1.** According to our efficient strategy we will execute Statements 1, 3 and 6 sequentially but together in the first step as only these statements make * specific assignment of a family member to a profession.* Mark that

*. Following is the result problem state in this step,*

**relationship takes secondary precedence here**As decided the five professions form the five rows and the logic table has two columns to record at most two family members having the same profession. Each row-column intersection has enough space to record three analysis results. For larger number of family members this space would have been more.

In the first step we have recorded just the results of processing the statements. Breakthroughs will come later based on this data.

Notice that we have jotted down the names of seven family members at the top left of the logic table to keep track of the members who have already been assigned to a profession and who are left to be assigned. The assigned member names are colored red (in actual exam we will cross-out the assigned names). We will shortly see how this action of keeping track of who are left to be assigned helps analysis in a significant way.

**Step 2.** Out of the three statements left we will execute the statement 4 and statement 5 together as these two contain more information than the statement 2. The result is shown below. Explanation will follow.

The content of statement 4 is duly noted against profession doctor without analysis or drawing any conclusion. But analyzing statement 5 we could conclude that F's sister is the second farmer and also the wife of A. We could not decide who is this F's sister but could be sure that it would be one of C, D or G. This subset of possible members has been deduced from the reasoning chain, "Four candidates C, D, F, G are left to be assigned > F's sister must be one of C, D or G."

**Step 3.** The last statement 2 will be processed at this step. Final assignments are shown below. Explanations will follow.

G's sister is a teacher. So there are two sisters out of C, D, F and G. Out of these 4 members, C has a brother E; F has a sister as also G. So * D is the single child, daughter-in-law of A and is the doctor.* This implies

**two of C, F, or G are sisters.****Resolving status of C**

C has a brother E. So if C is one of the two sisters out of C, F or G, the family members E, C and either of F or G are siblings. If these three siblings are children of A along with daughter B they form four children of A that violates given condition. On the other hand, if these three siblings are not children of A, number of children of A can be maximum of 2, which again violates the given condition of 2 sons and 1 daughter B of A. Thus C cannot be one of two sisters out of C, F or G. This implies F and G are the two sisters and C is the second son of A, the other son being E.

*Without going through this involved logic,* * if we assume C as one of the sons of A*, the condition of 2 sons and 1 daughter of A is neatly satisfied. This implies F and G as the two sisters which again fits in with the state of the logic table.

As every profession must belong to at least one family member, the remaining yet-to-be-assigned-to profession of business goes to C (F being the teacher and G, the wife of A being the farmer).

**Note:** If an assumption in logic analysis satisfies all the conditions of a logic table, that must be the solution. Here it is assumed that the logic problem does not have two solutions. In that case, we call the problem as malformed. Sometimes in actual test environment solution through such an assumption is the faster and better approach. Through the detailed logic analysis in resolving the status of C we have justified the solution formally.

Answering the five questions should not take much time now.

#### Answers

**Question 3-1.** Who is C's sister?

Answer 3-1. Option 3: B.

**Question 3-2.** What is G's profession?

Answer 3-2. Option 4: Farmer.

**Question 3-3.** Who is F's husband?

Answer 3-3. Option 4: Data insufficient.

**Question 3-4.** Which of the statements below is definitely wrong?

Answer 3-4. Option 3: C is F's sister.

**Question 3-5.** Which of the statements below is definitely correct?

Answer 3-5. Option 4: G is a mother.

### Recommendation

The * collapsed column logic analysis technique* is a structured, systematic, clear, and

*for analyzing logic puzzles and other types of logic analysis problems of any complexity with ease, speed and confidence without being confused. But one must be thoroughly conversant with variations of this class of problems by solving the puzzles, family relation or other types of problems using this efficient method. Without solving a sufficient number of such logic assignment problems during timed practice sessions one may not gain enough confidence and ability to solve a tricky logic puzzle or logic analysis question in an important competitive test.*

**efficient framework**### Tip

A powerful method of * enhancing useful pattern identification and logic analysis skill*, Play

**Sudoku**in a controlled manner. But beware, this great learning game, popularly called Rubik's Cube of 21st Century, is addictive.

To learn how to play Sudoku, you may refer to our **Sudoku pages***starting from the very beginning and proceeding to hard level games.*

You may refer to the following reading list on SBI PO level Reasoning puzzles of various types.

### Reading list on SBI PO and Bank PO level Reasoning puzzles

#### Tutorials

**How to solve SBI PO level logic puzzles in a few simple steps 1**

** How to solve SBI PO level logic puzzles in a few simple steps 2 **

**How to solve SBI PO level floor stay Reasoning Puzzle in a few confident steps 4**

**How to solve high level circular seating reasoning puzzles for SBI PO in confident steps 5 **

**How to solve high level hard two row seating reasoning puzzles for SBI PO in confident steps 6**

#### Solved reasoning puzzles

**SBI PO type high level floor stay reasoning puzzle solved in a few confident steps 1**

**SBI PO type high level reasoning puzzle solved in a few confident steps 2 **

**SBI PO type high level reasoning puzzle solved in a few confident steps 3**

**SBI PO type high level circular seating reasoning puzzle solved in confident steps 4**

**SBI PO type high level hard reasoning puzzle solved in confident steps 5**

**SBI PO type high level one to many valued group based reasoning puzzle solved in confident steps 6**

**SBI PO type high level hard two in one circular seating reasoning puzzle solved in confident steps 7**

**SBI PO type hard facing away circular seating reasoning puzzle solved in confident steps 8 **

**SBI PO type high level four dimensional reasoning puzzle solved in confident steps 9 **

**SBI PO type hard two row seating reasoning puzzle solved in confident steps 10 **

**Bank PO type two row hybrid reasoning puzzle solved in confident steps 1**