#### True False TellerT

True False teller questions are also known as binary logic questions. They form a part of the Data Interpretation and Logical Reasoning part of the CAT question paper. Even though binary logic questions have not been seen in abundance in previous years in CAT paper, at least 1 to 2 questions are present in all the PGDM/MBA entrance exams like SNAP, IIFT and NMAT including CAT. The concept is a part of the CAT exam curriculum and the student is expected to know how to solve these questions as the questions are not very difficult to crack and also less time consuming when compared to other concepts.

Below are the details about the concept for different competitive MBA exam:

CAT :

 True/False Teller (Binary Logic) Year No of Questions Good attempt Difficulty 2019 Slot 1 1 1 Moderate Slot 2 1 1 Moderate 2018 Slot 1 1 1 Moderate Slot 2 1 1 Easy 2017 Slot 1 1 1 Moderate Slot 2 1 1 Moderate

SNAP :

 True/False Teller (Binary Logic) Year Number of Questions Good attempt Difficulty 2019 1 1 Easy 2018 1 1 Easy 2017 1 1 Easy

### List of Concepts in that Chapter

The questions on True false teller or binary logic are based on the understanding of the arithmetic operators AND, OR and NOT. There are only two possible outcomes- True and False, also known as 0 and 1 in the computer language. In questions related to this concept, people answer in 2 to 3 statements in which some statements are true and some are false. The people, based on their statements can be classified as follows:

Truth-teller: He always will speak the truth and all the statements spoken by him are true.

Lie-teller: He will always lie and all the statements spoken by him are false.

Switcher: This person keeps on shifting between lies and truth that keep on changing on an alternate basis which means if his first statement is true, second is false and vice versa.

Let us understand this concept of binary logic with the help of an example:

Mohan went to a city on which there were three kinds of people. People of one kind always spoke the truth. People of the second kind always lied. People who belonged to the third kind spoke the truth and lie alternately. The city had only 3 fruits i.e. apple, mango and banana. Mohan found three people X, Y and Z asked them about their favourite fruits.

Their responses were as follows.

X: I like apples. Y likes mango

Y: Z likes mango. X likes banana

Z: I like apples. X likes banana

If it is known that X, Y and Z belonged to different kinds of people and each one of them liked a different fruit, then answer the following questions.

Who likes apple?

a) X

b) Y

c) Z

d) cannot be determined

Who belongs to the kind of truth-tellers?

a) X

b) Y

c) Z

d) cannot be determined

Who belongs to the kind of switchers?

a) X

b) Y

c) Z

d) cannot be determined

Solution:

Let us assume that Y belongs to the kind of people who always speak the truth. Therefore, we can say that Z likes mango and X likes banana, so Y must like apples. Once we have established this, we will check if the statements by other people validate our assumption or not. X says I like apple which is incorrect since we have established that Y likes apple. His second statement is that Y likes mangoes. This statement is also false since Y likes apples. Hence, both the statements of X are wrong and therefore he must belong to the kind of people who are liars. Now if our assumption is correct then Z must be the switcher. Z’s first statement is incorrect since Y likes apple. Z’s second statement is that X likes banana. This is true. Hence the statements validate our assumption. Therefore, Y is the truth-teller, Z is the switcher and X is the liar. Therefore, Z likes mango and X likes banana and Y likes apple.

### Some Questions from Previous Papers

Q1. There are 3 closed cartons in a room. One of the cartons contains cash. There is a printed message that is displayed outside each carton. Only one message is True and the other two messages are False. The first carton has the message: Cash is not in the Carton. The second carton has the message: No cash in the Carton. The third carton has the message: Cash is in the second carton. Which carton has the cash? (SNAP 2018)

A. First

B. Second

C. Third

D. Cannot be determined

Only one message is true and the other two are false.

If the second carton has the cash, then there will be two true messages which would be first and third.

If the third carton has the cash, then there will be two true messages which would be first and second.

If the first carton has the cash, then there will be one true message which would be second.

Hence, option A is correct.

Q2. Ramesh, Suresh and Mahesh are three people who belong to three different tribes of people. The three tribes are known as knights (those who always speak the truth), Knaves (who always lie) and switchers (those who alternatively speak the truth and lie). Ramesh said that Suresh is not a switcher. Mahesh said that Ramesh is a switcher. (SNAP 2015)

Who among the following is Knave?

A. Suresh

B. Ramesh

C. Mahesh

D. Cannot be determined

Because we only have 3 people, we should list down all the cases possible. Let T denote the knights, L denote the knaves, and S denote the switcher. Then possible arrangements are TLS, TSL, STL, SLT, LST, LTS. Ramesh said that Suresh is not a switcher, so it would be safe to remove TSL and LTS. Hence we are left with 4 cases which are TLS, STL, SLT,LST.

Now, Mahesh says that Ramesh is a switcher, therefore cases LST and STL can also be removed. So we will have two cases left:TLS and SLT.

From this, it can be deferred that Ramesh can either be a knight or a switcher, Suresh is a knave and Mahesh can also be either knight or a switcher.

Q3. Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items. (CAT 2019-SLOT 1)

The following additional facts are known

i. No composer who assigned an item to Princess, assigned any item to Queen

ii. No composer who assigned an item to Rani, assigned any item to Samragni

iii. The first performance was by Princess; this item was assigned by Badal

iv. The last performance was by Rani; this item was assigned by Gagan

v. The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same

Which of the following is true?

1. The third performance was composed by Ashman

2. The second performance was composed by Gagan

3. The third performance was composed by Dyu

4. The second performance was composed by Dyu

Which of the following is FALSE?

1. Princess did not perform in any item composed by Dyu

2. Queen did not perform in any item composed by Gagan

3. Samragni did not perform in any item composed by Ashman

4. Rani did not perform in any item composed by Badal

The sixth performance was composed by:

1. Gagan

2. Dyu

4. Ashman

Which pair of performances were composed by the same composer?

1. The first and the sixth

2. The first and the seventh

3. The second and the sixth

4. The third and the seventh

First of all represent the dancers and composers by the first letter of their respective name. As there were total 8 performances. No dancer performed her second item before the performance of the first item by any other dancers. So from point v) The items assigned by A were performed consecutively . It means Items assigned by A were performed at no 4 and 5. From point iv) The last performance was by Rani so she must have performed the 4th performance.

similarly from point iii) The first performance was by Princess; this item was assigned by Badal so 5th performance must be performed by P. This can be represented in the table as given below:

 Order of performance Dancer Composer 1 P B 2 3 4 R A 5 P A 6 7 8 R G
Now from point v) The number of performances between items assigned by each of the remaining composers was the same. this can not be 1 (because items assigned by A were consecutive ) similarly this can not be 2 or 3 as well if The number of performances between items assigned by each of the remaining composers was 2 or 3 then B must assign performance 4 or 5 which is not possible . thus this no must be 4. So B must assign performance 6 and g must assign performance no 3 . so the only performances left are 2 and 7 which must be assigned by D. Now the complete table will look like –
 Order of performance Dancer Composer 1 P B 2 S D 3 Q G 4 R A 5 P A 6 S B 7 Q D 8 R G
All the questions can be answered now.

A similar level of difficulty is expected for CAT 2021.

### How to deal with that topic preparation

For the understanding of the candidate, the preparation is divided into 3:

Level 1:

For level 1 preparation candidates need to gain a basic understanding of the concept of binary logic. Logical reasoning topics are all about practice because no formulas need to be remembered. Therefore, to approach the topic, take a question and try to extract all the information given. Pay heed to the constraints and try different assumptions to see what works and what contradicts. Take the help of the basic framework explained above. Developing critical thinking is an essential objective in this level of preparation.

Level 2:

When the candidate reaches this level, the expectation is that he has solved the basic questions and is clear with the concept and approach. Now, the focus should be on the structured thinking which helps the student reduce the number of cases possible through the process of elimination. Here, in binary logic concepts, if one starts by assuming a truth-teller, the question usually becomes easy and less time-consuming.

Level 3:

This level focusses on time management and solving the previous year CAT questions by timing oneself. Here, the candidate should be ready for approaching questions that have a high level of difficulty. CAT questions from this topic are usually easy and a candidate can score full marks in this concept, hence, this topic should be well prepared through question-solving and analysis.