Binary Logic Introduction & Solved Questions

When it comes to Binary Logic questions, you’ll notice that people respond to a question in two or three different ways. Some of these assertions are correct, while others are not. You must determine the real category of people based on the information provided. The binary search logic has to be found by contemplating the provided data in the statements by truth-tellers and liars. The use of this binary search logic is more in determining whether or not the statements presented are true.

Table Of Contents

1. What Is Binary Logic?
2. Assumptions In Binary Logic
3. Binary Logic Questions Types
4. Solved Examples
5. FAQs
6. Conclusion
7. Reference

What Is Binary Logic? 

In binary logic questions, people either say something true or something wrong. There are three types of people in this group:

1. Truth-teller: A truth-teller is supposed to speak the truth always. Every statement made by a truth-teller is always true.
2. Liar: A liar is supposed to speak the lies always. Every statement made by a liar always is false.
3. Alternator An alternator person alternates between telling the truth and lying. If this person’s initial assertion is correct, the second will be incorrect, the third will be correct, and so on. Similarly, if this person’s first statement is false, the second will be true, the third will be false, and so on. This person makes no specific amount of truthful or false assertions, but the order is always FALSE-TRUE-FALSE or TRUE-FALSE-TRUE.  

It’s all about making certain assumptions in binary logic questions (kind of assumptions are described later). These assumptions may result in certain inconsistencies, which are evidence that our assumptions are incorrect. If we don’t obtain a single contradiction for any assumption, we’ve found the answer to the provided binary logic problem.

A collection of principles for dealing with statements that must be true or false is known as binary logic. All binary logic systems have three operations in common: AND, OR, and NOT. Many logic systems also have the procedures  IF AND ONLY IF, IF….. THEN, and EOR. Because notations differ so much, it’s critical to be consistent when writing out binary logic.

Assumptions In Binary Logic

It’s all about making certain assumptions in binary logic questions.

These assumptions may result in certain inconsistencies, which are evidence that our assumptions are incorrect.

If we don’t obtain a single contradiction for any assumption, we’ve found the answer to the provided binary logic problem.

Binary Logic Questions Types

Binary Logic Questions will have people who will make statements. The overall pattern is for each of them to make three statements. The number of people can vary from 3 to 5, but if we go by the trend of the CAT exam; only 3 people’s problems have been asked in previous years.

The question will now specify how many of them are a truth-teller, a liar, or an alternator. We don’t always have someone who fits into each group.

In some circumstances, all three can be alternators, two alternators or one truth-teller, and so on. When the number of people is increased to four or five, the problem becomes even more intricate, requiring more iterations. Though CAT hasn’t introduced any four to five people problems. 

Solved Questions

Question 1. Three persons A, B, and C gave these statements:

A: – either Green Party or Freedom Party won the elections.

B: – Freedom Party won the elections.

C: – neither Green Party nor Freedom Party won the elections.

Of all these three persons A, B, and C, only one of them is wrong.

Who won the elections?

Answer: Because only one individual is incorrect, the other two are stating the truth. Assuming the Freedom Party won the election. As a result, A and B’s statements are true because they satisfy our criterion that the two of them are truth-tellers. As a result, the Freedom Party triumphs in the election.

If you think the Green Party won the election, propositions B and C become untrue, and the provided condition is violated.

Question 2. Tolu, Molu, and Golu were caught by police yesterday after one of them was suspected of robbing a local bank. Following extensive questioning, the three suspects made the following statements:

Tolu: –  I’m not guilty.

Molu: –  I’m not guilty.

Golu: – Molu is the one who is to blame.

If just one of the three claims is true, who among the three robbed the bank?

Answer: Let’s suppose that Molu is the thief. As a result, we can observe that Tolu’s remark is correct. However, Molu’s statement is incorrect. Golu’s allegation is also valid because he is pointing to Molu as the robber. As a result, the two statements are true, indicating a violation of the provided condition.

Assume that Tolu is the thief. The remaining two statements, except for Molu’s, are now false. Tolu, then, is the thief.

Conclusion

Binary Logic is one of the most important topics in the reasoning section of the CAT exam. Binary logic has the advantage of providing a set of formal rules that may be used to check for inconsistencies in statements (propositions). Two problems based on Binary Logic should be found among the 10 questions in Logical Reasoning. The use of this logic is more in determining whether or not the statements presented are true. It allows for neither true nor untrue claims, as well as statements with varying degrees of truthfulness.