Binary logic Basic concepts for CAT exam

CAT stands for common aptitude test. CAT Binary logic is important and useful in logical section. This topic is an integral part of many competitive exams. An aspirants could except few questions from this topic. As Logical reasoning section contain a total of 20 questions and out of that few questions are from Binary logic . A Logical Reasoning & Data Interpretation contains 30% weightage in CAT exams.

Questions from this section are frequently asked as per pervious paper analysis. To solve the questions based on Binary logic in CAT, candidates first have to understand the concept. Binary logic questions requires a candidate to develop a logical approach towards solving questions.

We can solve Binary logic questions easily if candidate pay attention while reading the question. Read the article to know more about some tricks, concepts, and solved sample questions. Generally, CAT questions are based on the given data, you need to figure out the actual category of persons.

Also read: How to Prepare for CAT 2022

Concepts of Binary logic Topic for CAT exam.

In a series of posts, we are going to cover the basics of some DI/LR topics. The first topic of discussion is Binary Logic. In a problem, we have people who either speak a true statement or a false statement. Hence these people are divided into three categories:

1. Truth-teller: This person will always speak the truth. All the statements made by this person are true.
2. Liar: This person will always tell a lie. All statements made by this person are false.
3. Alternator: This person always alternates between the truth and the lie. If first statement of this person is true, then second will be false, third will be true and so on. Similarly, if first statement made by this person is false, then second will be true, third will be false and so on. There is no particular number of true statements or false statements made by this person but order is always TRUE-FALSE-TRUE- or FALSE-TRUE-FALSE.

Binary logic questions are all about making some assumptions (kind of assumptions are described later). These assumptions may give rise to some contradictions which are the indicators that our assumptions are wrong. If for any assumption we do not get even a single contradiction, then that is the solution for the given problem.

Types of questions in Binary Logic Topic

Two types of questions based on Binary logic can be found in the Logical Reasoning section. The aspirant has to match the two logic propositions in each question.

For example Question Type – 1:

Two statements by each of the three persons are made in this type. One of the statements has got to be true and other is false. Now, one has to consider the two Propositions to arrive at the right answer.

1. The statement logic of the contents stated within
2. The ingredients i.e. the fact- one is true other will be naturally false or vice versa.

For example Question Type – 2:

If Two types of persons are found in this type of question.

1. Those who always speak the truth
2. Those who always tell a lie

Step Wise Solved example

For example 1: Three boys- Aman, Bagheer and Chiru replied to the question, “Who among you is a Doctor” in the following manner: We know exactly one of these boys is a Doctor, one is a Painter and one is an Athlete. Further, one always speaks the truth, one always lies and one alternates between the truth and the lie.

Video’s that could help aspirant.

Steps to solve Binary Logic

With the help of some statements made by these people we might be able to identify them without any assumption. Therefore Here is a list of 4 statements which one must always look out for to make the task easier. If any one of these is made by any person, then we can categorize them as explained below.

1. I am a liar:

Consider if a truth-teller says, “I am a liar”, which is a lie as a truth-teller can only say, “I am a truth-teller”. Hence, we can conclude that the person who said “I am a liar” is not the truth-teller.

Similarly, if a liar says that he/she is a liar then that statement will be true but the liar will always speak the lie. None of the statements made by him/her can be true. Then we can conclude this statement cannot be made by a liar.

The only category of person who can speak this statement can be the alternator. He can alternate between the truth and the lie. Since, he/she is not a liar but he/she can still make a false statement, alternator is the only category of people who can make the statement, “I am a liar”. Then statement in itself will be a lie. This gives us another hint that the statement proceeding and the statement preceding this statement will always be a true.

1. I am not a truth teller:

Similar to the explanation above, a truth-teller can never make this statement because if he/she makes this statement then it will be a lie which contradicts the fact that a truth-teller always speaks the truth.

If the liar makes the above statement, then it will be the truth for him which again contradicts the fact that a liar will always lie. Hence, a liar cannot make this statement.

The alternator can say, “I am not a truth-teller”, as he can say either the truth or the lie. So this statement will be a true statement for him, which gives us another hint that the statements preceding and proceeding this statement are the lie.

1. I am an alternator:

A truth-teller cannot make this statement as this statement will be a lie for him which conflicts the fact of the truth-teller. A liar can make this statement as this statement will be a lie for him/her. An alternator can also make this statement and this will be the truth for the alternator. We can conclude that this statement can be made by the liar or the alternator.

1. I am not an alternator:

Similarly to the above statement, a liar will not make this statement. A truth-teller can make this statement. An alternator can make this statement and this time it will be the lie for him/her.

Summary to explain Example 1

Step 1:

Step 2:

Now what if we do not have any of the above said 4 statements in any of the statements. In that case we will self assume their status and the assumption in which there is no contradiction will be the answer.