Binary logic Basic concepts for the CAT exam

Binary Logic is an essential concept for the Logical Reasoning and Data Interpretation (LRDI) section of the CAT exam. Binary logic problems involve logical reasoning based on binary conditions, typically represented by 1s and 0s, to help assess candidates' ability to think critically and solve problems efficiently.

In this article, we will discuss the fundamental concepts of Binary Logic, key rules, and strategies for mastering binary logic questions in the CAT exam.

What is Binary Logic?

Binary logic refers to the system of operations and problem-solving that involves two basic states—True (1) and False (0). These binary digits (bits) are used to build complex logical operations and relationships.

Binary logic is used in various fields, such as computer science, electronics, and mathematics, and is applied in CAT exam questions that require logical reasoning and interpretation.

Key Concepts in Binary Logic

1. Basic Operations in Binary Logic

Binary logic is built on simple operations, such as AND, OR, NOT, and XOR, which form the foundation of all binary logic problems.

2. Boolean Algebra

Boolean algebra is a branch of mathematics that deals with binary variables and logical operations. It provides the framework for solving binary logic problems. The key rules of Boolean algebra are:

• Identity Law: A ∧ 1 = A, A ∨ 0 = A
• Null Law: A ∧ 0 = 0, A ∨ 1 = 1
• Domination Law: A ∧ A = A, A ∨ A = A
• Complement Law: A ∧ ¬A = 0, A ∨ ¬A = 1
• Distributive Law: A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)

Example Problem:

If A = 1 and B = 0, then the expression A ∨ (B ∧ 1) will evaluate as follows:

A ∨ (B ∧ 1) = 1 ∨ (0 ∧ 1) = 1 ∨ 0 = 1

How Binary Logic is Tested in CAT Exam

Binary logic questions in the CAT exam may test your ability to identify correct sequences, patterns, or logical relationships based on binary operations. Here are common formats of binary logic questions in the CAT exam:

• True/False Statements: You may be given a series of binary statements and asked to identify the truth values based on logical operations.
• Puzzles and Seating Arrangements: Sometimes, you will be required to solve puzzles that involve binary conditions (e.g., at least one of two conditions must be true).
• Logical Reasoning Problems: These problems might ask you to deduce conclusions based on given logical statements or constraints.

Tips for Solving Binary Logic Problems in CAT Exam

1. Understand the Basics: First, ensure that you are clear on the basic logical operations (AND, OR, NOT, XOR) and their truth tables. Familiarity with Boolean algebra will also help you quickly simplify and solve binary logic problems.
2. Use Process of Elimination: In many binary logic questions, if you can’t immediately find the solution, use elimination to rule out incorrect answers and narrow down your choices.
3. Practice Logical Reasoning: Since binary logic is often tested in the form of logical reasoning questions, consistent practice with logical puzzles and reasoning problems will improve your speed and accuracy.
4. Break Down the Problem: When faced with complex binary logic problems, break them down into smaller, manageable parts. Apply the rules of logic step by step to reach the solution.

Common Mistakes to Avoid in Binary Logic Problems

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 the 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 assumptions. Therefore Here is a list of 4 statements that 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 with this statement are 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.