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Binary logic is a set of rules for dealing with logical arguments that must be true or untrue. The binary logical reasoning notion is used to frame the truth-teller, truth-liar, and alternator questions.
What Is Binary Logic?
People either say something true or something false in binary logic questions. This category consists of three categories of people:
Truth-teller: A truth-teller is expected to always tell the truth. A truth-statements teller’s are always correct.
Liar: A liar is expected to always tell lies. A liar’s every statement is always false.
Alternator A person who is an alternator switches between telling the truth and lying. If the first assertion is true, the second is false, the third is true, and so on. If this person’s first statement is untrue, the second will also be wrong, and so on. This person does not make a set number of true or false claims, but the order is always FALSE-TRUE-FALSE or TRUE-FALSE-TRUE.
In binary logic questions, it’s all about establishing certain assumptions (kind of assumptions are described later). Certain inconsistencies may arise as a result of these assumptions, indicating that our assumptions are erroneous. We’ve solved the binary logic problem if we don’t get a single contradiction for any of the assumptions.
Binary logic is a set of ideas for dealing with claims that must be true or false. Three operations are common to all binary logic systems: AND, OR, and NOT. The operations IF AND ONLY IF, IF….. THEN, and EOR are also included in many logic systems. Because there are so many different notations, consistency is crucial when writing binary logic.
Binary Logic Assumptions
In binary logic questions, it’s all about establishing certain assumptions.
Certain inconsistencies may arise as a result of these assumptions, indicating that our assumptions are erroneous.
We’ve solved the binary logic problem if we don’t get a single contradiction for any of the assumptions.
What is binary logic reasoning?
A collection of principles for dealing with propositions that must be true or untrue 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…. THEN, IF AND ONLY IF, and EOR.
Types of Binary Logic Questions
People will make statements in the Binary Logic Questions. Each of them is expected to deliver three statements in total. The number of people can range from three to five, although if the CAT exam is any indication, just three people’s difficulties have been asked in prior years.
The inquiry will now ask how many of them are truthful, liars, or alternators. We don’t always have someone who belongs in each of the groups.
In some cases, all three could be alternators, two could be alternators, one could be a truth-teller, and so on. The situation becomes considerably more complicated when the number of people is increased to four or five, necessitating further iterations. CAT hasn’t yet presented any four to five person issues.
Solved Examples of Binary Logic
Question 1: A, B, and C each made the following statements:
A: – the elections were won by either the Green Party or the Freedom Party.
B: – The Freedom Party was elected.
C: Neither the Green Party nor the Freedom Party were elected.
Only one of these three people, A, B, and C, is incorrect.
Who did the elections favour?
Sol:- Because only one person is erroneous, the other two are telling the truth. Assuming that the Freedom Party is elected.
As a result, A and B’s claims are correct since they meet our requirement of being truth-tellers. The Freedom Party wins the election as a result.
Propositions B and C become untrue if you believe the Green Party won the election, and the supplied condition is broken.
Question 2: Three people, A, B, and C, made the following statements:
According to A, the elections were won by either the Freedom Party or the Green Party.
According to B, the Freedom Party won.
Neither the Freedom Party nor the Green Party won the elections, according to C.
Only one of these people is incorrect.
Who did the elections favour?
1. The Libertarian Party
Green Party (#2)
3. Insufficient data
4. None of the following
Option 1 is correct.
Because only one person is erroneous, the other two are telling the truth. Assume the Freedom Party was victorious in the election. As a result, the statements A and B are correct because they meet our requirement of two 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 supplied condition is broken.
Question3 Tolu, Molu, and Golu were apprehended by the 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.
Molu is the one who is to blame, Golu.
If just one of the three claims is true, who of the three robbed the bank?
1.Molu
2.Tolu
3.Golu
4. None of the following
Option 2 is correct.
Solution: Let’s pretend Molu is the thief. As a result, Tolu’s assertion is correct. However, Molu’s remark is incorrect. Golu’s allegation is also valid because he is pointing to Molu as the robber. So two assertions are correct, indicating that the provided condition is violated.
Assume that Tolu is the thief. The following two statements, with the exception of Molu’s, become untrue. Tolu, then, is the thief.
Conclusion
One of the most essential concepts in the CAT reasoning part is binary logic. Binary logic provides the benefit of supplying a set of formal rules for detecting discrepancies in statements (propositions). Among the ten questions in Logical Reasoning, two problems based on Binary Logic should be found. This logic is mostly used to determine whether or not the statements offered are correct. It doesn’t distinguish between genuine and false assertions, as well as statements with varied degrees of truthfulness.
