CAT  >  Binary Logic- 1

# Binary Logic- 1 - Logical Reasoning (LR) and Data Interpretation (DI) - CAT

Instructions:
Mohan went to an Island on which there were three tribes of people. People from one of the tribes always spoke the truth. People from the second tribe always lied. People who belonged to the third tribe spoke truth and lie alternately. The Island 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 apple. Y likes mango
Y: Z likes mango. X likes banana
Z: I like apple. X likes banana
If it is known that X, Y and Z belonged to different tribes and each one of them liked a different fruit, then answer the following questions.
Question 1: Who likes apple?
a) X
b) Y
c) Z
d) cannot be determined
Solution:
Let us assume that Y belongs to the tribe which always speaks the truth.
So we know that Z likes mango and X likes banana, so Y must like apple.
Now let’s see if the statements by the other people validate or contradict our assumption. X says I like apple which is wrong since we know that Y likes apple. His second statement is that Y likes mangoes. This statement is also wrong since Y likes apples. So since both the statements of X are wrong, he must belong to the tribe of liars. Now if our assumption is correct then Z must be the alternator. Z’s first statement is wrong since Y likes apple. Z’s second statement is that X likes banana. This is true. Hence the statements validate our assumption. So Y is the truth teller, Z is the alternator and X is the lier. Also Z likes mango and X likes banana and Y likes apple.

Question 2: Who belongs to the tribe of truth tellers?
a) X
b) Y
c) Z
d) cannot be determined
Solution:
Let us assume that Y belongs to the tribe which always speaks the truth.
So we know that Z likes mango and X likes banana, so Y must like apple.
Now let’s see if the statements by the other people validate or contradict our assumption. X says I like apple which is wrong since we know that Y likes apple. His second statement is that Y likes mangoes. This statement is also wrong since Y likes apples. So since both the statements of X are wrong, he must belong to the tribe of liars. Now if our assumption is correct then Z must be the alternator. Z’s first statement is wrong since Y likes apple. Z’s second statement is that X likes banana. This is true. Hence the statements validate our assumption. So Y is the truth teller, Z is the alternator and X is the lier. Also Z likes mango and X likes banana and Y likes apple.

Question 3: Who belongs to the tribe of alternaters?
a) X
b) Y
c) Z
d) cannot be determined
Solution:
Let us assume that Y belongs to the tribe which always speaks the truth.
So we know that Z likes mango and X likes banana, so Y must like apple.
Now let’s see if the statements by the other people validate or contradict our assumption. X says I like apple which is wrong since we know that Y likes apple. His second statement is that Y likes mangoes. This statement is also wrong since Y likes apples. So since both the statements of X are wrong, he must belong to the tribe of liars. Now if our assumption is correct then Z must be the alternator. Z’s first statement is wrong since Y likes apple. Z’s second statement is that X likes banana. This is true. Hence the statements validate our assumption. So Y is the truth teller, Z is the alternator and X is the lier. Also Z likes mango and X likes banana and Y likes apple.

Question 4: 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 Alters(those who alternatively speak the truth and lie).
Ramesh said that Suresh is not an alter. Mahesh said that Ramesh is an alter.
Who among the following is Knave?

a) Suresh
b) Ramesh
c) Mahesh
d) Cannot be determined
In both the cases, Suresh is the Knave. So option A is correct
Solution:
Since we only have 3 people, we can list down the possible cases. Let T denote the knights, L denote the knaves, and A denotes the alters.
Then possible arrangements are
TLA, TAL, ATL, ALT, LAT, LTA
Ramesh said that Suresh is not an alter, so we can remove the cases TAL and LTA. This is because if Ramesh is a knight then Suresh can not be an alter and if Ramesh is a knave than Suresh is an alter. So we have 4 cases left which are
TLA, ATL, ALT,LAT
Mahesh says that Ramesh is an alter, so using this statement we can rule out cases LAT and ATL.
So we have two cases which are left these are TLA and ALT
From these cases, Ramesh can either be a knight or an alter, Suresh is a knave and Mahesh can also be either knight or an alter.

Question 5: Ramesh, Suresh and Mahesh are three people who belong to three different tribes. The three tribes are known as knights (those who always speak the truth), Knaves(who always lie) and Alters(those who alternatively speak the truth and lie).
Ramesh said that Suresh is not an alter. Mahesh said that Ramesh is an alter.
Who is the Knight?

a) Suresh
b) Ramesh
c) Mahesh
d) cannot be determined
So we cannot determine that who is the knight and who is alter. Hence correct option is cannot be determined.
Solution:
Since we only have 3 people, we can list down the possible cases. Let T denote the knights, L denote the knaves, and A denotes the alters.
Then possible arrangements are
TLA, TAL, ATL, ALT, LAT, LTA
Ramesh said that Suresh is not an alter, so we can remove the cases TAL and LTA. This is because if Ramesh is a knight then Suresh can not be an alter and if Ramesh is a knave than Suresh is an alter. So we have 4 cases left which are
TLA, ATL, ALT,LAT
Mahesh says that Ramesh is an alter, so using this statement we can rule out cases LAT and ATL.
So we have two cases which are left these are TLA and ALT
From these cases, Ramesh can either be a knight or an alter, Suresh is a knave and Mahesh can also be either knight or an alter.

The document Binary Logic- 1 | Logical Reasoning (LR) and Data Interpretation (DI) - CAT is a part of the CAT Course Logical Reasoning (LR) and Data Interpretation (DI).
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## Logical Reasoning (LR) and Data Interpretation (DI)

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## FAQs on Binary Logic- 1 - Logical Reasoning (LR) and Data Interpretation (DI) - CAT

 1. What is binary logic?
Ans. Binary logic is a fundamental concept in computer science and mathematics that deals with logical operations and values represented by two states, typically denoted as 0 and 1. It forms the basis of digital computing systems and is used to perform logical operations such as AND, OR, and NOT.
 2. How is binary logic used in computer programming?
Ans. Binary logic is extensively used in computer programming to make decisions and perform logical operations. It allows programmers to write code that can evaluate conditions and execute different sets of instructions based on the logical outcomes. Binary logic is crucial for tasks like flow control, error handling, and decision-making in programming.
 3. What are the basic logical operators in binary logic?
Ans. The basic logical operators in binary logic are AND, OR, and NOT. - AND: It returns true if both input values are true; otherwise, it returns false. - OR: It returns true if at least one of the input values is true; otherwise, it returns false. - NOT: It negates the input value. If the input is true, it returns false, and if the input is false, it returns true.
 4. How can binary logic be applied in real-life situations?
Ans. Binary logic finds applications in various real-life situations, especially in digital systems and electronics. It is used in designing circuits, computer processors, communication systems, and even in everyday devices like smartphones, calculators, and home appliances. Binary logic enables the representation and processing of information in a digital format, making it possible to store, transmit, and manipulate data efficiently.
 5. Are there any limitations or challenges in binary logic?
Ans. Although binary logic is a powerful tool, it does have limitations and challenges. One limitation is that it only represents two states (0 and 1), which may not be sufficient for certain complex scenarios that require more nuanced representation. Additionally, binary logic can be challenging to grasp for beginners, as it involves abstract thinking and understanding of logical concepts. However, with practice and familiarity, these challenges can be overcome.

## Logical Reasoning (LR) and Data Interpretation (DI)

125 videos|171 docs|117 tests

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