CAT prep: Use binary logic in finding truthfulness of statements in LR
**Logical Reasoning section in Common Admission Test (CAT) carries a couple of questions on binary logic. The application of this logic is more in finding out the truthfulness in the statements made.**

| 12 July 2013 0546 IST

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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.

Logical Reasoning section in Common Admission Test (CAT) carries a couple of questions on binary logic. The Binary logic derives its name from the Boolean logic which is the synonym to two-value logic system. In fact, it is the sub area of algebra called Boolean algebra in which the values of the variables are the truth values - *true* and *false. *

The binary logic is a set of rules for dealing with propositions that must be either true or false. There are three operations common to all binary logic systems, AND, OR, and NOT. In addition to that, many logic systems add the operations IF . . . THEN, IF AND ONLY IF, and EOR. Notations vary greatly, so it is important to remain consistent in how one writes out binary logic.

**Relevance to CAT –** The advantage of binary logic is that it provides a set of formal rules that can be used to test statements (propositions) for contradictions. Out of the ten questions in Logical Reasoning, one may expect to find two questions based on Binary Logic. The application of this logic is more in finding out the truthfulness in the statements made. It allows for statements that are neither true nor false and/or statements with degrees of truthfulness.

**How to crack the questions** – 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.

**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.

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

**Question Type – 2** – Two types of persons are found in this type of question.

- Those who always speak the truth
- Those who always tell a lie

**Example -**

A statement shall be either true or false, such as “The soldier is over six feet tall,” or “Three plus three equals seven.”

Subjective statements such as “Rohan is handsome,” generally cannot be treated as statements related to Binary Logic, as their truth depends on perception of thought. Such statements should also avoid pronouns, as a change in the pronoun’s referent changes the nature of the intended statement. Now, the negation operation, NOT, is a unitary operation that is applied to a single statement.

For a given statement A, NOT-A is false if A is true and NOT-A is true if A is false. The AND operation creates a new compound from two simpler statements, such as “The soldier is over six feet tall and three plus three equals seven.” This new proposition can be true if both of the propositions that make it up are true; otherwise it is false.

The OR operation also creates a new proposition from two simpler propositions, such as “The soldier is over six feet tall or three plus three equals seven.” A OR B is a true statement if A is true, if B is true, or if both are true. It is only false if both A and B are false. The conditional operation, IF A THEN B, is only false when A is true and B is false and true otherwise, so it can also be expressed as NOT-A OR B.

The IF AND ONLY IF operation, also called the biconditional operation, is true if A and B are both true and false if A and B have differing truth values. The EOR operation is a strict alternative, either A or B but not both. It is the opposite of the biconditional, true if A and B have differing values and false if they have matching truth values.

**Crack the CAT question –**

Direction – Answer the question based on the following information.

Four students (Ashish, Dhanraj, Felix and Sameer) sat for the Common Entrance Exam for Management (CEEM).

One student got admission offers from three National Institutes of Management (NIM), another in two NIMs, the third in one NIM, while the fourth got none. Below are some of the facts about who got admission offers from how many NIMs and what is their educational background

- The one who is an engineer didn’t get as many admissions as Ashish.
- The one who got offer for admissions in two NIMs isn’t Dhanraj nor is he a chartered accountant.
- Sameer is an economist
- Dhanraj isn’t an engineer and received more admission offers than Ashish.
- The medical doctor got the most number of admission offers.

Which one of the following statements is necessarily true?

- Ashish is a chartered accountant and got offer for admission in three NIMs.
- Dhanraj is a medical doctor and got admission offer in one NIM.
- Sameer is an economist who got admission offers in two NIMs.
- Felix who is not an engineer did not get any offer for admission.

Ans. – (c) – Explanation – Understand by analyzing the information – and eliminate the other possibilities.

Sameer – Economist with 2 offers

Felix – engineer with 0/1 offer

Dhanraj – Doctor – 0/1 offer

Ashish – Chartered Accountant – 3 offers.

With the analysis, the answer becomes self-explanatory i.e. (c).

*Author of this article Mr S K Agarwal is a CAT Expert, a seasoned CAT trainer with over 25 years of experience, & author of many CAT books. He also guides Verbal Ability and LR Section to CAT Aspirants through MBAUniverse.com online coaching classes. ** *Visit the link below for more information and new batch schedules:

http://www.mbauniverse.com/mba-exam-preparation/CAT_Preparation/mba_preparation_package.php